Singular field of a scalar point particle

We give a fourth order approximation to the singular field of a point scalar charge in various spacetimes. In all cases, this depends on the position and four velocity of the particle and on the position where the field is evaluated. We use the following definitions:

r1 - particle’s radial position
θ1 - particle’s polar coordinate (assumed to be π/2)
ϕ1 - particle’s azimuthal coordinate

r - radial position where the field is evaluated
θ - polar position where the field is evaluated
ϕ - azimuthal position where the field is evaluated

Δr = r - r1
Δθ = θ - θ1 = θ-π/2
Δϕ = ϕ - ϕ1
ΔQ = sin(Δϕ/2)
ΔR = sin(Δϕ)

ur1, ut1, uϕ1 - components of the particle’s four-velocity (assume uθ1=0)

e1 = (Subscript[u, t]) - “energy” constant of motion
l1 = (Subscript[u, ϕ]) - “angular momentum” constant of motion

M - mass of the central black hole
a - spin of the central black hole (in units of M)

Schwarzschild

Generic (equatorial) geodesic

Note that the four-velocity of a general equatorial geodesic in Schwarzschild may be given in terms of the constants of motion:

(ur1^2)=(e1^2)+(((2 M-r1) ((l1^2)+(r1^2)))/(r1^3))
ut1=e1 (r1/(r1-2M))
uϕ1=(l1/(r1^2))

We have used this fact to simplify the following expression for the singular field

ΦsSchwarzschildEquatorial=(64*(l1^2+r1^2)^3*ΔQ^6+(32*(l1^2+r1^2)*(l1^4*(-4*M+r1)-r1^4*(2*M+r1*ur1^2)+l1^2*r1^2*(-6*M+r1+2*r1*ur1^2))*ΔQ^8)/r1+(r1^3*(-2*M+r1+r1*ur1^2)^3*Δr^6)/(-2*M+r1)^6+(M*r1^2*(-2*M+r1+r1*ur1^2)^3*Δr^7)/(2*(-2*M+r1)^7)-(M*r1*(-2*M+r1+r1*ur1^2)^2*(6*M^2+M*r1*(-7+4*e1^2-3*ur1^2)+2*r1^2*(1-e1^2+ur1^2))*Δr^8)/(4*(-2*M+r1)^8)-(M*(-2*M+r1+r1*ur1^2)^2*(12*M^3+2*M^2*r1*(-11+4*e1^2+3*ur1^2)+2*M*r1^2*(7-2*ur1^2-5*ur1^4+e1^2*(-5+9*ur1^2))+r1^3*(-3+5*ur1^4+2*ur1^6+e1^2*(3-9*ur1^2-6*ur1^4)))*Δr^9)/(8*(-2*M+r1)^9)+32*l1*r1*(l1^2+r1^2)^2*ur1*ΔQ^6*ΔR-(16*l1*ur1*(4*l1^8*M+18*l1^6*M*r1^2+3*l1^4*(12*M-r1)*r1^4+3*r1^8*(2*M+r1*ur1^2)+l1^2*r1^6*(28*M-r1*(3+2*ur1^2)))*ΔQ^8*ΔR)/r1^4+(6*l1*r1^3*ur1*(-2*M+r1+r1*ur1^2)^2*Δr^5*ΔR)/(-2*M+r1)^5+(l1*(9*M-2*r1)*r1^2*ur1*(-2*M+r1+r1*ur1^2)^2*Δr^6*ΔR)/(2*(-2*M+r1)^6)-(l1*M*ur1*(4*l1^2*(2*M-r1)*(-(r1*(1+ur1^2))+2*M*(2+ur1^2))+r1*(44*M^3+4*M^2*r1*(-10+4*e1^2-7*ur1^2)-3*r1^3*(1+ur1^2)^2+3*M*r1^2*(5+6*ur1^2+ur1^4)))*Δr^7*ΔR)/(2*(2*M-r1)^7)+(l1*M*ur1*(2*r1*(72*M^4+8*M^3*r1*(3+7*e1^2-15*ur1^2)+r1^4*(1+ur1^2)^2*(-1+13*ur1^2+10*ur1^4)+2*M^2*r1^2*(-27+48*ur1^2+67*ur1^4)-2*M*r1^3*(-7+27*ur1^2+67*ur1^4+33*ur1^6))+l1^2*(-8*M^3*(-49+39*ur1^2)+4*M^2*r1*(-105+110*ur1^2+91*ur1^4)+r1^3*(-21+32*ur1^2+91*ur1^4+38*ur1^6)-2*M*r1^2*(-77+103*ur1^2+182*ur1^4+38*ur1^6)))*Δr^8*ΔR)/(8*r1*(-2*M+r1)^8)+48*r1^2*(l1^2+r1^2)^2*ΔQ^4*Δθ^2-(8*(l1^6*(8*M-4*r1)-4*l1^4*r1^2*(-7*M+r1*(3+ur1^2))+2*r1^6*(4*M+r1*(-1+2*ur1^2))+l1^2*r1^4*(28*M-r1*(10+3*ur1^2)))*ΔQ^6*Δθ^2)/r1+8*l1*r1*(l1^2+r1^2)*(l1^2+3*r1^2)*ur1*ΔQ^4*ΔR*Δθ^2+(4*l1*ur1*(l1^4*r1^2*(328*M^2-178*M*r1+7*r1^2)+2*(2*M-r1)*r1^6*(12*M+r1+6*r1*ur1^2)+2*l1^2*(2*M-r1)*r1^4*(63*M-r1*(4+3*ur1^2))+4*l1^6*M*(34*M+r1*(-17-5*e1^2+5*ur1^2)))*ΔQ^6*ΔR*Δθ^2)/(r1^2*(-2*M+r1))+12*r1^4*(l1^2+r1^2)*ΔQ^2*Δθ^4-(2*r1*(l1^4*(132*M^2-4*(29+3*e1^2)*M*r1+r1^2*(25+6*ur1^2))+l1^2*(2*M-r1)*r1^2*(108*M-r1*(41+9*ur1^2))+(2*M-r1)*r1^4*(36*M+r1*(-13+18*ur1^2)))*ΔQ^4*Δθ^4)/(6*M-3*r1)+(4*l1^3*r1^3*ur1+6*l1*r1^5*ur1)*ΔQ^2*ΔR*Δθ^4+(l1*ur1*(l1^4*(900*M^2+22*r1^2-2*M*r1*(247+105*e1^2-105*ur1^2))+2*l1^2*(2*M-r1)*r1^2*(315*M-r1*(13+9*ur1^2))+(2*M-r1)*r1^4*(108*M+r1*(23+54*ur1^2)))*ΔQ^4*ΔR*Δθ^4)/(3*(-2*M+r1))+r1^6*Δθ^6+(-4*l1^4*M*r1-(2*r1^5*(6*M+r1*(-2+3*ur1^2)))/3+(l1^2*r1^3*(-60*M+r1*(14+3*ur1^2)))/6)*ΔQ^2*Δθ^6+(l1*r1^5*ur1*ΔR*Δθ^6)/2-(l1*ur1*(276*l1^4*M+l1^2*r1^2*(462*M-r1*(11+6*ur1^2))+4*r1^4*(18*M+r1*(7+9*ur1^2)))*ΔQ^2*ΔR*Δθ^6)/12+((-12*l1^2*M*r1^3+r1^5*(-6*M+r1-3*r1*ur1^2))*Δθ^8)/24-(l1*r1^2*ur1*(126*l1^2*M+r1^2*(18*M+r1*(11+9*ur1^2)))*ΔR*Δθ^8)/48+Δr^4*((12*r1^2*(-2*M+r1+r1*ur1^2)*(r1^2*(-2*M+r1+r1*ur1^2)+l1^2*(-2*M+r1+5*r1*ur1^2))*ΔQ^2)/(-2*M+r1)^4+(3*r1^4*(-2*M+r1+r1*ur1^2)^2*Δθ^2)/(-2*M+r1)^4)+Δr^5*((2*r1*(-2*M+r1+r1*ur1^2)*(-2*l1^2*(3*M-r1)*(2*M-r1*(1+5*ur1^2))+r1^2*(-8*M^2+2*M*r1*(3+ur1^2)+r1^2*(-1+ur1^4)))*ΔQ^2)/(-2*M+r1)^5+(r1^3*(-2*M+r1+r1*ur1^2)^2*(4*M+r1*(-1+ur1^2))*Δθ^2)/(2*(-2*M+r1)^5))+Δr^6*(((r1^3*(-2*M+r1+r1*ur1^2)^2*(M^2-4*M*r1+4*r1^2*ur1^2)+8*l1^4*M*(2*M-r1)*(-(r1*(1+3*ur1^2))+M*(4+6*ur1^2))+l1^2*r1*(-28*M^4+2*M^3*r1*(62+16*e1^2-85*ur1^2)+4*r1^4*(-1+ur1^2+2*ur1^4)-4*M*r1^3*(-8+17*ur1^2+19*ur1^4)+M^2*r1^2*(-103+189*ur1^2+92*ur1^4)))*ΔQ^2)/(2*r1*(-2*M+r1)^6)-((2*M-r1*(1+ur1^2))*(8*l1^2*M*(-2*M+r1)^2+r1^2*(-2*M^3+4*r1^3*ur1^2*(1+ur1^2)+M^2*r1*(9+ur1^2)-4*M*r1^2*(1+3*ur1^2)))*Δθ^2)/(8*(-2*M+r1)^6))+Δr^7*((M*((2*M-r1)*r1^3*(-2*M+r1+r1*ur1^2)^2*(23*M^2+26*M*r1*(-1+3*ur1^2)-4*r1^2*(-1+10*ur1^2+6*ur1^4))-4*l1^4*(2*M-r1)*(12*M^3*(27+5*ur1^2)+2*M^2*r1*(-129-60*ur1^2+140*ur1^4)+M*r1^2*(91+75*ur1^2-280*ur1^4-98*ur1^6)+r1^3*(-12-15*ur1^2+70*ur1^4+49*ur1^6))+l1^2*r1*(216*M^5-4*M^4*r1*(785+152*e1^2-167*ur1^2)-2*M^3*r1^2*(-1945+70*ur1^2+546*ur1^4)+M^2*r1^3*(-2003+191*ur1^2+1690*ur1^4+560*ur1^6)+4*r1^5*(-13+6*ur1^2+41*ur1^4+35*ur1^6+13*ur1^8)-4*M*r1^4*(-128+29*ur1^2+225*ur1^4+140*ur1^6+26*ur1^8)))*ΔQ^2)/(4*r1^2*(-2*M+r1)^8)-(M*(-4*l1^2*(8*M^4*(-49+3*ur1^2)-4*M^3*r1*(-130+7*ur1^2+10*ur1^4)+2*M^2*r1^2*(-140+3*ur1^2+30*ur1^4-14*ur1^6)-r1^4*(8+ur1^2-5*ur1^4+7*ur1^6+5*ur1^8)+M*r1^3*(75+3*ur1^2-30*ur1^4+28*ur1^6+10*ur1^8))+r1*(520*M^5+44*M^4*r1*(3+8*e1^2-18*ur1^2)-4*r1^5*(1+ur1^2)^2*(-1+10*ur1^2+6*ur1^4)+2*M^3*r1^2*(-241+432*ur1^2+385*ur1^4)-M^2*r1^3*(-227+662*ur1^2+1157*ur1^4+348*ur1^6)+2*M*r1^4*(-25+117*ur1^2+293*ur1^4+175*ur1^6+24*ur1^8)))*Δθ^2)/(16*(-2*M+r1)^8))+Δr^3*((16*l1*r1^2*ur1*(2*l1^2*r1*ur1^2+3*(l1^2+r1^2)*(-2*M+r1+r1*ur1^2))*ΔQ^2*ΔR)/(-2*M+r1)^3+(12*l1*r1^4*ur1*(-2*M+r1+r1*ur1^2)*ΔR*Δθ^2)/(-2*M+r1)^3)+Δr^4*((-2*l1*r1*ur1*(2*l1^2*(5*M-2*r1)*(6*M-r1*(3+5*ur1^2))+r1^2*(40*M^2-2*M*r1*(17+5*ur1^2)+r1^2*(7+2*ur1^2-5*ur1^4)))*ΔQ^2*ΔR)/(-2*M+r1)^4+(l1*r1^3*ur1*(-2*M+r1+r1*ur1^2)*(20*M+r1*(-7+5*ur1^2))*ΔR*Δθ^2)/(2*(-2*M+r1)^4))+Δr^5*((l1*ur1*(8*l1^4*M*(-2*M+r1)+l1^2*r1*(-74*M^3+4*r1^3*(1+4*ur1^2)-4*M*r1^2*(8+23*ur1^2)+M^2*r1*(85-16*e1^2+120*ur1^2))+r1^3*(-98*M^3+M^2*r1*(149+45*ur1^2)+2*M*r1^2*(-35-30*ur1^2+ur1^4)+2*r1^3*(5+8*ur1^2+3*ur1^4)))*ΔQ^2*ΔR)/(r1*(-2*M+r1)^5)+(l1*ur1*(8*l1^2*M*(-2*M+r1)^2+r1^2*(-98*M^3+M^2*r1*(157+45*ur1^2)+2*M*r1^2*(-39-34*ur1^2+ur1^4)+4*r1^3*(3+5*ur1^2+2*ur1^4)))*ΔR*Δθ^2)/(4*(-2*M+r1)^5))+Δr^6*((l1*ur1*(-4*l1^4*M*(2*M-r1)*(20*M^2*(-19+7*ur1^2)-7*M*r1*(-29+20*ur1^2+18*ur1^4)+r1^2*(-36+35*ur1^2+63*ur1^4))-(2*M-r1)*r1^3*(14*M^4+M^3*r1*(-47+253*ur1^2)-8*r1^4*(-1+ur1^2+2*ur1^4)-22*M^2*r1^2*(-2+13*ur1^2+11*ur1^4)+4*M*r1^3*(-7+27*ur1^2+36*ur1^4+14*ur1^6))+l1^2*r1*(-204*M^5+4*M^4*r1*(917+236*e1^2-459*ur1^2)+8*r1^5*(3-2*ur1^2)+M^3*r1^2*(-3923+1606*ur1^2-224*ur1^4)-4*M*r1^4*(79-65*ur1^2+14*ur1^4+21*ur1^6)+2*M^2*r1^3*(803-518*ur1^2+112*ur1^4+84*ur1^6)))*ΔQ^2*ΔR)/(4*r1^2*(-2*M+r1)^7)-(l1*ur1*(r1*(1220*M^5+2*M^4*r1*(-226+312*e1^2-565*ur1^2)+8*r1^5*(2+ur1^2-ur1^4)+M^3*r1^2*(-295+761*ur1^2+484*ur1^4)+4*M*r1^4*(-25+11*ur1^2+38*ur1^4+14*ur1^6)-2*M^2*r1^3*(-122+187*ur1^2+257*ur1^4+56*ur1^6))+4*l1^2*M*(8*M^3*(65+3*ur1^2)-6*M^2*r1*(91+6*ur1^2+28*ur1^4)-r1^3*(26+3*ur1^2+42*ur1^4+35*ur1^6)+M*r1^2*(195+18*ur1^2+168*ur1^4+70*ur1^6)))*ΔR*Δθ^2)/(16*(2*M-r1)^7))+Δr^2*((48*r1*(l1^2+r1^2)*(4*l1^2*r1*ur1^2+(l1^2+r1^2)*(-2*M+r1+r1*ur1^2))*ΔQ^4)/(-2*M+r1)^2+(24*r1^3*(2*l1^2*r1*ur1^2+(l1^2+r1^2)*(-2*M+r1+r1*ur1^2))*ΔQ^2*Δθ^2)/(-2*M+r1)^2+(3*r1^5*(-2*M+r1+r1*ur1^2)*Δθ^4)/(-2*M+r1)^2)+Δr^3*((8*(l1^4*(9*M-4*r1)*(2*M-r1*(1+5*ur1^2))+2*l1^2*r1^2*(14*M^2-M*r1*(13+15*ur1^2)+r1^2*(3+6*ur1^2-5*ur1^4))-r1^4*(-10*M^2+M*r1*(9+ur1^2)+2*r1^2*(-1+ur1^4)))*ΔQ^4)/(2*M-r1)^3+(4*r1^2*(r1^2*(-10*M^2+M*r1*(9+ur1^2)+2*r1^2*(-1+ur1^4))+l1^2*(-14*M^2+M*r1*(13+15*ur1^2)+r1^2*(-3-6*ur1^2+5*ur1^4)))*ΔQ^2*Δθ^2)/(-2*M+r1)^3+(r1^4*(-2*M+r1+r1*ur1^2)*(5*M+2*r1*(-1+ur1^2))*Δθ^4)/(2*(-2*M+r1)^3))+Δr^4*((2*(4*l1^6*M*(8*M^2-6*M*r1+r1^2)+l1^4*r1*(44*M^4+4*M^3*r1*(-19+4*e1^2-115*ur1^2)+4*r1^4*(1+12*ur1^2)-4*M*r1^3*(7+78*ur1^2)+M^2*r1^2*(67+654*ur1^2))+l1^2*(2*M-r1)*r1^3*(36*M^3-3*M^2*r1*(22+79*ur1^2)+2*M*r1^2*(17+99*ur1^2-6*ur1^4)+r1^3*(-5-34*ur1^2+15*ur1^4))+(2*M-r1)*r1^5*(30*M^3-M^2*r1*(47+3*ur1^2)-2*M*r1^2*(-11-6*ur1^2+ur1^4)-r1^3*(3+4*ur1^2+3*ur1^4+2*ur1^6)))*ΔQ^4)/(r1^2*(-2*M+r1)^5)+((-8*l1^4*M*(8*M^2-6*M*r1+r1^2)+l1^2*r1*(-136*M^4+2*M^3*r1*(112-16*e1^2+269*ur1^2)-4*r1^4*(2+20*ur1^2+7*ur1^4)+M^2*r1^2*(-170-849*ur1^2+16*ur1^4)+2*M*r1^3*(31+229*ur1^2+24*ur1^4))-2*(2*M-r1)*r1^3*(30*M^3-3*M^2*r1*(17+ur1^2)-2*M*r1^2*(-13-8*ur1^2+ur1^4)-2*r1^3*(2+3*ur1^2+2*ur1^4+ur1^6)))*ΔQ^2*Δθ^2)/(2*(2*M-r1)^5)+(r1^2*(-90*M^3*r1+2*r1^4*(5+7*ur1^2+5*ur1^4+3*ur1^6)+M^2*(48*l1^2*ur1^2+r1^2*(145+9*ur1^2))+2*M*r1*(-6*l1^2*ur1^2*(2+ur1^2)+r1^2*(-35-20*ur1^2+3*ur1^4)))*Δθ^4)/(24*(-2*M+r1)^4))+Δr^5*(-(((-2*l1^6*M*(2*M-r1)*(20*M^2*(17+7*ur1^2)+r1^2*(31+35*ur1^2-70*ur1^4)+2*M*r1*(-89-70*ur1^2+70*ur1^4))+(2*M-r1)*r1^5*(72*M^4+2*M^3*r1*(-57+35*ur1^2)+M^2*r1^2*(53-108*ur1^2-89*ur1^4)+8*r1^4*ur1^2*(-2-ur1^2+ur1^4)+M*r1^3*(-7+72*ur1^2+49*ur1^4+18*ur1^6))+l1^2*(2*M-r1)*r1^3*(724*M^4+2*M^3*r1*(-610+121*ur1^2)-4*r1^4*(-4+19*ur1^2+5*ur1^4)+M^2*r1^2*(727-505*ur1^2+370*ur1^4)-M*r1^3*(181-358*ur1^2+195*ur1^4+98*ur1^6))+2*l1^4*r1*(716*M^5-2*M^4*r1*(1152+108*e1^2-49*ur1^2)+12*r1^5*(-1+2*ur1^2)+M^3*r1^2*(2147-69*ur1^2+560*ur1^4)+2*M*r1^4*(85-74*ur1^2+70*ur1^4+91*ur1^6)-M^2*r1^3*(879-264*ur1^2+560*ur1^4+364*ur1^6)))*ΔQ^4)/(r1^3*(-2*M+r1)^6))-((2*(2*M-r1)*r1^3*(72*M^4+2*M^3*r1*(-59+35*ur1^2)+M^2*r1^2*(65-112*ur1^2-89*ur1^4)+2*r1^4*(1-7*ur1^2-5*ur1^4+3*ur1^6)+2*M*r1^3*(-8+35*ur1^2+28*ur1^4+9*ur1^6))-4*l1^4*M*(8*M^3*(67+39*ur1^2)-12*M^2*r1*(46+39*ur1^2+35*ur1^4)+6*M*r1^2*(32+39*ur1^2+70*ur1^4+35*ur1^6)-r1^3*(25+39*ur1^2+105*ur1^4+105*ur1^6))+l1^2*r1*(712*M^5-4*M^4*r1*(985+168*e1^2-161*ur1^2)+4*r1^5*(-7+15*ur1^2+4*ur1^4)+2*M^3*r1^2*(2015-262*ur1^2+618*ur1^4)+8*M*r1^4*(44-49*ur1^2+32*ur1^4+21*ur1^6)-M^2*r1^3*(1711-813*ur1^2+1194*ur1^4+336*ur1^6)))*ΔQ^2*Δθ^2)/(4*r1*(-2*M+r1)^6)-((r1^2*(216*M^4+2*M^3*r1*(-173+105*ur1^2)+M^2*r1^2*(171-328*ur1^2-267*ur1^4)+2*r1^4*(1-23*ur1^2-13*ur1^4+11*ur1^6)+2*M*r1^3*(-15+107*ur1^2+77*ur1^4+27*ur1^6))+6*l1^2*M*(152*M^3-128*M^2*r1*(2+ur1^2)+2*M*r1^2*(71+70*ur1^2+62*ur1^4)-r1^3*(26+38*ur1^2+65*ur1^4+35*ur1^6)))*Δθ^4)/(48*(2*M-r1)^5))+Δr*((96*l1*r1*(l1^2+r1^2)^2*ur1*ΔQ^4*ΔR)/(-2*M+r1)+(48*l1*r1^3*(l1^2+r1^2)*ur1*ΔQ^2*ΔR*Δθ^2)/(-2*M+r1)+(6*l1*r1^5*ur1*ΔR*Δθ^4)/(-2*M+r1))+Δr^2*((8*l1*ur1*(l1^4*(21*M-10*r1)+r1^4*(9*M-4*r1+6*r1*ur1^2)+2*l1^2*r1^2*(15*M+r1*(-7+5*ur1^2)))*ΔQ^4*ΔR)/(-2*M+r1)^2+(4*l1*r1^2*ur1*(r1^2*(9*M-4*r1+6*r1*ur1^2)+l1^2*(15*M+r1*(-7+5*ur1^2)))*ΔQ^2*ΔR*Δθ^2)/(-2*M+r1)^2+(l1*r1^4*ur1*(9*M-4*r1+6*r1*ur1^2)*ΔR*Δθ^4)/(2*(-2*M+r1)^2))+Δr^3*((-8*l1*ur1*(l1^4*(29*M^2-31*M*r1+8*r1^2)+l1^2*r1^2*(52*M^2+r1^2*(13-5*ur1^2)+M*r1*(-53+2*ur1^2))+r1^4*(31*M^2-M*r1*(30+ur1^2)+r1^2*(7+ur1^2+2*ur1^4)))*ΔQ^4*ΔR)/((2*M-r1)^3*r1)-(2*l1*r1*ur1*(l1^2*(60*M^2-M*r1*(67+2*ur1^2)+2*r1^2*(9+4*ur1^2))+2*r1^2*(31*M^2-M*r1*(34+ur1^2)+r1^2*(9+3*ur1^2+2*ur1^4)))*ΔQ^2*ΔR*Δθ^2)/(2*M-r1)^3+(l1*r1*ur1*(12*l1^2*M*(-2*M+r1+r1*ur1^2)-r1^2*(93*M^2-M*r1*(104+3*ur1^2)+2*r1^2*(14+5*ur1^2+3*ur1^4)))*ΔR*Δθ^4)/(6*(2*M-r1)^3))+Δr^4*(-((l1*ur1*(14*l1^6*M*(2*M-r1)*(4*M*(7+ur1^2)-r1*(7+2*ur1^2))+(2*M-r1)*r1^5*(124*M^3+M^2*r1*(-239+275*ur1^2)+M*r1^2*(167-227*ur1^2-38*ur1^4)+2*r1^3*(-19+15*ur1^2+10*ur1^4))-2*l1^4*r1*(262*M^4-24*r1^4-M^3*r1*(591+196*e1^2+532*ur1^2)-2*M*r1^3*(-32+91*ur1^2+133*ur1^4)+2*M^2*r1^2*(99+364*ur1^2+266*ur1^4))-l1^2*(2*M-r1)*r1^3*(58*M^3+M^2*r1*(331-930*ur1^2)-2*r1^3*(-53+ur1^2)+M*r1^2*(-397+515*ur1^2+490*ur1^4)))*ΔQ^4*ΔR)/(r1^3*(-2*M+r1)^5))-(l1*ur1*(2*(2*M-r1)*r1^3*(124*M^3+M^2*r1*(-261+275*ur1^2)+2*r1^3*(-19+12*ur1^2+7*ur1^4)-2*M*r1^2*(-89+102*ur1^2+19*ur1^4))+28*l1^4*M*(8*M^2*(7+10*ur1^2)+r1^2*(7+20*ur1^2+25*ur1^4)-2*M*r1*(21+40*ur1^2+25*ur1^4))+l1^2*r1*(476*M^4+4*r1^4*(21+2*ur1^2)+4*M^3*r1*(50+196*e1^2+667*ur1^2)+M^2*r1^2*(181-3454*ur1^2-1680*ur1^4)+8*M*r1^3*(-46+106*ur1^2+105*ur1^4)))*ΔQ^2*ΔR*Δθ^2)/(4*r1*(-2*M+r1)^5)-(l1*ur1*(r1^2*(-372*M^3+33*M^2*r1*(23-25*ur1^2)-2*r1^3*(-57+52*ur1^2+37*ur1^4)+2*M*r1^2*(-261+344*ur1^2+57*ur1^4))+6*l1^2*M*(244*M^2-2*M*r1*(131+199*ur1^2)+r1^2*(70+208*ur1^2+175*ur1^4)))*ΔR*Δθ^4)/(48*(-2*M+r1)^4))+Δr*((32*(l1^2+r1^2)*(l1^4*(4*M-2*r1)+r1^4*(2*M+r1*(-1+ur1^2))+l1^2*r1^2*(6*M+r1*(-3+5*ur1^2)))*ΔQ^6)/(r1*(-2*M+r1))-(8*r1*(5*l1^4*(2*M+r1*(-1+ur1^2))+3*r1^4*(2*M+r1*(-1+ur1^2))+4*l1^2*r1^2*(4*M+r1*(-2+3*ur1^2)))*ΔQ^4*Δθ^2)/(2*M-r1)+(2*r1^3*(l1^2*(8*M-4*r1+6*r1*ur1^2)+3*r1^2*(2*M+r1*(-1+ur1^2)))*ΔQ^2*Δθ^4)/(-2*M+r1)+(r1^5*(-2*M+r1-r1*ur1^2)*Δθ^6)/(4*M-2*r1))+Δr^2*((8*(4*l1^6*(6*M^2-7*M*r1+2*r1^2)+2*l1^4*r1^2*(30*M^2+3*r1^2*(3-5*ur1^2)-M*r1*(33+4*ur1^2))+r1^6*(16*M^2+2*M*r1*(-7+3*ur1^2)+r1^2*(3-4*ur1^2+ur1^4))+l1^2*r1^4*(52*M^2-4*M*r1*(13+6*ur1^2)+r1^2*(13-23*ur1^2+12*ur1^4)))*ΔQ^6)/(r1^2*(-2*M+r1)^2)+(2*(l1^4*(76*M^2+4*r1^2*(6+7*ur1^2)-2*M*r1*(43+16*ur1^2))+4*l1^2*r1^2*(30*M^2-M*r1*(33+14*ur1^2)+3*r1^2*(3+ur1^2+2*ur1^4))+r1^4*(48*M^2+2*M*r1*(-25+9*ur1^2)+r1^2*(13-8*ur1^2+3*ur1^4)))*ΔQ^4*Δθ^2)/(-2*M+r1)^2+((24*l1^4*M*(2*M-r1*(1+3*ur1^2))+r1^4*(144*M^2+2*M*r1*(-77+27*ur1^2)+r1^2*(41-22*ur1^2+9*ur1^4))+l1^2*r1^2*(252*M^2-4*M*r1*(61+30*ur1^2)+r1^2*(59+75*ur1^2+36*ur1^4)))*ΔQ^2*Δθ^4)/(6*(-2*M+r1)^2)+(r1^5*(4*M^2*(11+12*e1^2-33*ur1^2)+r1^2*(11-10*ur1^2+3*ur1^4)-2*M*r1*(22-43*ur1^2-9*ur1^4+12*e1^2*(1+ur1^2)))*Δθ^6)/(24*(-2*M+r1)^3))+Δr^3*((-4*(28*l1^8*M*(2*M-r1)*(-(r1*(1+3*ur1^2))+M*(4+6*ur1^2))-4*l1^6*r1*(112*M^4-4*r1^4-28*M^3*r1*(7+e1^2+10*ur1^2)+M*r1^3*(2-77*ur1^2-105*ur1^4)+2*M^2*r1^2*(41+154*ur1^2+105*ur1^4))-l1^2*(2*M-r1)*r1^5*(212*M^3-2*M^2*r1*(94+207*ur1^2)+r1^3*(13-54*ur1^2+ur1^4)+M*r1^2*(15+343*ur1^2+258*ur1^4))-l1^4*(2*M-r1)*r1^3*(432*M^3+2*r1^3*(11-23*ur1^2)-10*M^2*r1*(37+76*ur1^2)+M*r1^2*(33+495*ur1^2+700*ur1^4))-(2*M-r1)*r1^7*(20*M^3-2*M^2*r1*(5+22*ur1^2)+M*r1^2*(-10+23*ur1^2-11*ur1^4)+r1^3*(5+2*ur1^2+11*ur1^4-2*ur1^6)))*ΔQ^6)/(r1^4*(-2*M+r1)^4)+((-4*l1^6*M*(12*M^2*(12+35*ur1^2)+r1^2*(18+105*ur1^2+175*ur1^4)-2*M*r1*(54+210*ur1^2+175*ur1^4))+l1^2*(2*M-r1)*r1^3*(528*M^3-2*M^2*r1*(253+516*ur1^2)-3*r1^3*(-5+20*ur1^2+ur1^4)+M*r1^2*(91+667*ur1^2+608*ur1^4))-4*l1^4*r1*(-188*M^4+2*r1^4*(2+ur1^2)+2*M^3*r1*(202+36*e1^2+379*ur1^2)+2*M*r1^3*(10+101*ur1^2+175*ur1^4)-M^2*r1^2*(211+827*ur1^2+700*ur1^4))+(2*M-r1)*r1^5*(60*M^3-2*M^2*r1*(13+66*ur1^2)+M*r1^2*(-28+63*ur1^2-33*ur1^4)+r1^3*(13+6*ur1^2+35*ur1^4-6*ur1^6)))*ΔQ^4*Δθ^2)/(r1^2*(-2*M+r1)^4)+((-12*l1^4*M*(2*M^2*(61+225*ur1^2)+r1^2*(16+117*ur1^2+175*ur1^4)-M*r1*(93+459*ur1^2+350*ur1^4))+l1^2*r1*(1128*M^4-4*M^3*r1*(827+174*e1^2+1059*ur1^2)+4*r1^4*(1+27*ur1^2+28*ur1^4)+6*M^2*r1^2*(355+918*ur1^2+442*ur1^4)-M*r1^3*(387+1737*ur1^2+1550*ur1^4))+(2*M-r1)*r1^3*(180*M^3-4*M^2*r1*(19+99*ur1^2)+M*r1^2*(-83+186*ur1^2-99*ur1^4)+2*r1^3*(19+9*ur1^2+53*ur1^4-9*ur1^6)))*ΔQ^2*Δθ^4)/(12*(-2*M+r1)^4)+(r1*(12*l1^2*M*(26*M^2-M*r1*(29+51*ur1^2)+r1^2*(8+27*ur1^2+23*ur1^4))+r1^2*(60*M^3-4*M^2*r1*(7+33*ur1^2)+M*r1^2*(-29+66*ur1^2-33*ur1^4)+2*r1^3*(7+3*ur1^2+17*ur1^4-3*ur1^6)))*Δθ^6)/(48*(2*M-r1)^3))+Δr*((16*l1*ur1*(-6*l1^4*M+r1^4*(-8*M+r1+r1*ur1^2)+l1^2*r1^2*(-14*M+r1+4*r1*ur1^2))*ΔQ^6*ΔR)/(-2*M+r1)+(4*l1*ur1*(l1^4*(-14*M+8*r1)+4*l1^2*r1^2*(-9*M+2*r1*(2+ur1^2))+3*r1^4*(-8*M+r1*(3+ur1^2)))*ΔQ^4*ΔR*Δθ^2)/(-2*M+r1)+(l1*ur1*(24*l1^4*M+r1^4*(72*M-r1*(35+9*ur1^2))+l1^2*r1^2*(90*M-r1*(35+12*ur1^2)))*ΔQ^2*ΔR*Δθ^4)/(6*M-3*r1)+(l1*r1^5*ur1*(-2*M*(11+12*e1^2-9*ur1^2)+r1*(11+3*ur1^2))*ΔR*Δθ^6)/(12*(-2*M+r1)^2))+Δr^2*((-4*l1*ur1*(44*l1^8*M*(-2*M+r1)+4*l1^6*M*r1*(116*M^2-2*M*r1*(69+11*e1^2+36*ur1^2)+r1^2*(40+47*ur1^2))+l1^2*(2*M-r1)*r1^5*(130*M^2-r1^2*(1+3*ur1^2)-M*r1*(65+366*ur1^2))+l1^4*(2*M-r1)*r1^3*(376*M^2+6*r1^2-M*r1*(201+476*ur1^2))+(2*M-r1)*r1^7*(10*M^2-M*r1*(4+81*ur1^2)+r1^2*(-1-ur1^2+6*ur1^4)))*ΔQ^6*ΔR)/(r1^4*(-2*M+r1)^3)-(l1*ur1*(-84*l1^6*M*(2*M-r1)*(2+5*ur1^2)+4*l1^4*r1*(222*M^3+4*r1^3+2*M*r1^2*(41+147*ur1^2)-3*M^2*r1*(97+28*e1^2+168*ur1^2))+l1^2*(2*M-r1)*r1^3*(488*M^2+r1^2*(-37+ur1^2)-M*r1*(173+1008*ur1^2))+(2*M-r1)*r1^5*(30*M^2+M*r1*(34-243*ur1^2)+r1^2*(-25-5*ur1^2+18*ur1^4)))*ΔQ^4*ΔR*Δθ^2)/(r1^2*(-2*M+r1)^3)+(l1*ur1*(-12*l1^4*M*(2*M-r1)*(52+175*ur1^2)+l1^2*r1*(1092*M^3+2*r1^3*(19-56*ur1^2)-4*M^2*r1*(556+303*e1^2+1074*ur1^2)+M*r1^2*(763+2978*ur1^2))+(2*M-r1)*r1^3*(90*M^2+M*r1*(175-729*ur1^2)+2*r1^2*(-58-3*ur1^2+27*ur1^4)))*ΔQ^2*ΔR*Δθ^4)/(12*(2*M-r1)^3)+(l1*r1*ur1*(36*l1^2*M*(19*M-r1*(10+23*ur1^2))+r1^2*(30*M^2+M*r1*(61-243*ur1^2)+2*r1^2*(-22+3*ur1^2+9*ur1^4)))*ΔR*Δθ^6)/(48*(-2*M+r1)^2))+Δr*((-16*(8*l1^10*M*(-2*M+r1)+4*l1^8*M*r1*(28*M^2-2*M*r1*(16+2*e1^2+9*ur1^2)+r1^2*(9+11*ur1^2))+2*l1^6*(2*M-r1)*r1^3*(54*M^2-r1^2-M*r1*(25+77*ur1^2))+l1^4*(2*M-r1)*r1^5*(80*M^2-r1^2*(1+3*ur1^2)-2*M*r1*(19+100*ur1^2))+(2*M-r1)*r1^9*(4*M^2-r1^2*ur1^2*(1+3*ur1^2)-2*M*(r1+6*r1*ur1^2))+l1^2*(2*M-r1)*r1^7*(32*M^2-6*M*r1*(3+20*ur1^2)+r1^2*(1+5*ur1^2+6*ur1^4)))*ΔQ^8)/(r1^5*(-2*M+r1)^2)-(4*(-28*l1^8*M*(2*M-r1)*(1+5*ur1^2)+8*l1^6*r1*(26*M^3+r1^3+3*M*r1^2*(2+21*ur1^2)-M^2*r1*(29+7*e1^2+119*ur1^2))+l1^4*(2*M-r1)*r1^3*(184*M^2+r1^2*(-13+5*ur1^2)-2*M*r1*(33+338*ur1^2))+2*(2*M-r1)*r1^7*(8*M^2-2*M*(r1+12*r1*ur1^2)-r1^2*(1+ur1^2+6*ur1^4))+2*l1^2*(2*M-r1)*r1^5*(54*M^2-M*r1*(23+201*ur1^2)+r1^2*(-2+11*ur1^2+9*ur1^4)))*ΔQ^6*Δθ^2)/(r1^3*(-2*M+r1)^2)-((-6*l1^6*M*(2*M-r1)*(13+175*ur1^2)+2*l1^4*r1*(228*M^3+r1^3*(8-37*ur1^2)+2*M*r1^2*(32+601*ur1^2)-2*M^2*r1*(137+39*e1^2+1089*ur1^2))+2*l1^2*(2*M-r1)*r1^3*(198*M^2-M*r1*(91+729*ur1^2)+r1^2*(-4+51*ur1^2+27*ur1^4))+(2*M-r1)*r1^5*(72*M^2-2*M*r1*(5+108*ur1^2)-r1^2*(13+5*ur1^2+54*ur1^4)))*ΔQ^4*Δθ^4)/(3*r1*(-2*M+r1)^2)+((36*l1^4*M*(-2*M+r1+23*r1*ur1^2)+4*r1^4*(-12*M^2+2*M*(r1+18*r1*ur1^2)+r1^2*(2+ur1^2+9*ur1^4))-l1^2*r1^2*(204*M^2-2*M*r1*(58+369*ur1^2)+r1^2*(7+51*ur1^2+18*ur1^4)))*ΔQ^2*Δθ^6)/(24*M-12*r1)+(r1^2*(-18*l1^2*M*(2*M-r1*(1+7*ur1^2))+r1^2*(-12*M^2+4*M*(r1+9*r1*ur1^2)+r1^2*(1+2*ur1^2+9*ur1^4)))*Δθ^8)/(96*M-48*r1)))/Sqrt[4*(l1^2+r1^2)*ΔQ^2+(r1*(-2*M+r1+r1*ur1^2)*Δr^2)/(-2*M+r1)^2+(2*l1*r1*ur1*Δr*ΔR)/(-2*M+r1)+r1^2*Δθ^2];

Circular geodesic

For a circular geodesic, we have:

ur1=0
ut1=((Sqrt[r1])/(Sqrt[r1-3M]))
uϕ1=((Sqrt[M])/(r1(Sqrt[r1-3M])))

along with
e1=((r1-2 M)/((Sqrt[r1]) (Sqrt[-3 M+r1])))
l1=r1((Sqrt[M])/(Sqrt[r1-3M]))

ΦsSchwarzschildCircular=((64*r1^6*(-2*M+r1)^3*ΔQ^6)/(-3*M+r1)^3+(r1^3*Δr^6)/(-2*M+r1)^3+(48*r1^6*(-2*M+r1)^2*ΔQ^4*Δθ^2)/(-3*M+r1)^2+(12*r1^6*(-2*M+r1)*ΔQ^2*Δθ^4)/(-3*M+r1)+r1^6*Δθ^6+Δr^4*((12*r1^4*ΔQ^2)/(6*M^2-5*M*r1+r1^2)+(3*r1^4*Δθ^2)/(-2*M+r1)^2)+Δr^2*((48*r1^5*(-2*M+r1)*ΔQ^4)/(-3*M+r1)^2+(24*r1^5*ΔQ^2*Δθ^2)/(-3*M+r1)+(3*r1^5*Δθ^4)/(-2*M+r1)))/(4*(r1^2+(M*r1^2)/(-3*M+r1))*ΔQ^2+(r1*Δr^2)/(-2*M+r1)+r1^2*Δθ^2)^(7/2)+((M*r1^2*Δr^7)/(2*(-2*M+r1)^4)+Δr^5*((-2*r1^3*ΔQ^2)/(-2*M+r1)^2-(r1^3*(-4*M+r1)*Δθ^2)/(2*(-2*M+r1)^3))+Δr^3*((8*(3*M-2*r1)*r1^4*ΔQ^4)/(-3*M+r1)^2-(8*r1^4*ΔQ^2*Δθ^2)/(-3*M+r1)+((5*M-2*r1)*r1^4*Δθ^4)/(2*(-2*M+r1)^2))+Δr*((32*(M-r1)*r1^5*(-2*M+r1)^2*ΔQ^6)/(-3*M+r1)^3-(8*(4*M-3*r1)*(2*M-r1)*r1^5*ΔQ^4*Δθ^2)/(-3*M+r1)^2-(2*r1^5*(-5*M+3*r1)*ΔQ^2*Δθ^4)/(-3*M+r1)-(r1^5*Δθ^6)/2))/(4*(r1^2+(M*r1^2)/(-3*M+r1))*ΔQ^2+(r1*Δr^2)/(-2*M+r1)+r1^2*Δθ^2)^(7/2)+((-32*M*r1^5*(-2*M+r1)^3*ΔQ^8)/(-3*M+r1)^3+(M^2*r1*(-M+r1)*Δr^8)/(4*(2*M-r1)^5*(3*M-r1))+(16*r1^5*(-2*M+r1)^2*(5*M^2-4*M*r1+r1^2)*ΔQ^6*Δθ^2)/(-3*M+r1)^3+(2*r1^5*(222*M^4-459*M^3*r1+346*M^2*r1^2-112*M*r1^3+13*r1^4)*ΔQ^4*Δθ^4)/(3*(-3*M+r1)^3)+(r1^5*(-30*M^3+57*M^2*r1-29*M*r1^2+4*r1^3)*ΔQ^2*Δθ^6)/(3*(-3*M+r1)^2)-(r1^5*(6*M^2-9*M*r1+r1^2)*Δθ^8)/(72*M-24*r1)+Δr^6*(-(M*r1^2*(31*M^2-37*M*r1+8*r1^2)*ΔQ^2)/(2*(-3*M+r1)^2*(-2*M+r1)^3)+(M*r1^2*(19*M^2-21*M*r1+4*r1^2)*Δθ^2)/(8*(3*M-r1)*(-2*M+r1)^4))+Δr^4*((2*r1^3*(-65*M^3+74*M^2*r1-26*M*r1^2+3*r1^3)*ΔQ^4)/((-3*M+r1)^3*(-2*M+r1))+((-50*M^3*r1^3+72*M^2*r1^4-30*M*r1^5+4*r1^6)*ΔQ^2*Δθ^2)/(6*M^2-5*M*r1+r1^2)^2+(5*r1^3*(9*M^2-10*M*r1+2*r1^2)*Δθ^4)/(24*(-2*M+r1)^3))+Δr^2*((8*r1^4*(-2*M+r1)*(15*M^2-10*M*r1+3*r1^2)*ΔQ^6)/(-3*M+r1)^3+(2*r1^4*(37*M^2-40*M*r1+13*r1^2)*ΔQ^4*Δθ^2)/(-3*M+r1)^2+(r1^4*(294*M^3-498*M^2*r1+259*M*r1^2-41*r1^3)*ΔQ^2*Δθ^4)/(6*(2*M-r1)*(-3*M+r1)^2)+(r1^4*(48*M^2-57*M*r1+11*r1^2)*Δθ^6)/(24*(6*M^2-5*M*r1+r1^2))))/(4*(r1^2+(M*r1^2)/(-3*M+r1))*ΔQ^2+(r1*Δr^2)/(-2*M+r1)+r1^2*Δθ^2)^(7/2)+((M^2*(2*M^2-2*M*r1+r1^2)*Δr^9)/(8*(3*M-r1)*(-2*M+r1)^6)+Δr^7*(-(M*r1*(89*M^3-73*M^2*r1+10*M*r1^2+4*r1^3)*ΔQ^2)/(4*(-3*M+r1)^2*(-2*M+r1)^4)+(M*r1*(-19*M^3+7*M^2*r1+6*M*r1^2-4*r1^3)*Δθ^2)/(16*(2*M-r1)^5*(3*M-r1)))+Δr^5*((M*r1^2*(-195*M^3+207*M^2*r1-83*M*r1^2+9*r1^3)*ΔQ^4)/((-3*M+r1)^3*(-2*M+r1)^2)+(r1^2*(-279*M^4+307*M^3*r1-86*M^2*r1^2-12*M*r1^3+4*r1^4)*ΔQ^2*Δθ^2)/(4*(-3*M+r1)^2*(-2*M+r1)^3)+(r1^2*(132*M^4-75*M^3*r1-41*M^2*r1^2+32*M*r1^3-2*r1^4)*Δθ^4)/(48*(3*M-r1)*(-2*M+r1)^4))+Δr^3*((-4*r1^3*(139*M^4-163*M^3*r1+78*M^2*r1^2-27*M*r1^3+5*r1^4)*ΔQ^6)/(-3*M+r1)^4-(r1^3*(357*M^4-434*M^3*r1+230*M^2*r1^2-78*M*r1^3+13*r1^4)*ΔQ^4*Δθ^2)/((-3*M+r1)^3*(-2*M+r1))-(r1^3*(732*M^4-1074*M^3*r1+677*M^2*r1^2-239*M*r1^3+38*r1^4)*ΔQ^2*Δθ^4)/(12*(6*M^2-5*M*r1+r1^2)^2)+(r1^3*(-66*M^3+69*M^2*r1-43*M*r1^2+14*r1^3)*Δθ^6)/(48*(3*M-r1)*(-2*M+r1)^2))+Δr*((-16*M*r1^4*(-2*M+r1)^2*(29*M^3-25*M^2*r1+3*M*r1^2+r1^3)*ΔQ^8)/(-3*M+r1)^5-(4*r1^4*(-2*M+r1)*(97*M^4-86*M^3*r1+27*M^2*r1^2-8*M*r1^3+2*r1^4)*ΔQ^6*Δθ^2)/(-3*M+r1)^4-(r1^4*(312*M^4-351*M^3*r1+193*M^2*r1^2-73*M*r1^3+13*r1^4)*ΔQ^4*Δθ^4)/(3*(-3*M+r1)^3)+(r1^4*(54*M^3-51*M^2*r1+31*M*r1^2-8*r1^3)*ΔQ^2*Δθ^6)/(12*(-3*M+r1)^2)+(r1^5*(3*M+r1)*Δθ^8)/(48*(3*M-r1))))/(4*(r1^2+(M*r1^2)/(-3*M+r1))*ΔQ^2+(r1*Δr^2)/(-2*M+r1)+r1^2*Δθ^2)^(7/2);

Kerr

Equatorial geodesic

Note that the four-velocity of a general equatorial geodesic in Kerr may be given in terms of the constants of motion:

(ur1^2)=(e1^2)-1-2(-(M/r1)+(((l1^2)-(a^2)((e1^2)-1))/(2(r1^2)))-((M(((l1-a e1))^2))/(r1^3)))
ut1=(1/((r1^2)-2M r1+(a^2)))(((r1^2)+(a^2)+((2M (a^2))/r1))e1-((2M a)/r1)l1)
uϕ1=(1/((r1^2)-2M r1+(a^2)))((1-((2M)/r1))l1+((2M a)/r1)e1)

We have used this fact to simplify the following expression for the singular field

ΦsKerrEquatorial=(64*(l1^2+r1^2+(a^2*(2*M+r1))/r1)^3*ΔQ^6+(r1^6*(a^2+r1*(-2*M+r1+r1*ur1^2))^3*Δr^6)/(a^2+r1*(-2*M+r1))^6+(6*l1*r1^6*ur1*(a^2+r1*(-2*M+r1+r1*ur1^2))^2*Δr^5*ΔR)/(a^2+r1*(-2*M+r1))^5+48*(a^2*(2*M+r1)+r1*(l1^2+r1^2))^2*ΔQ^4*Δθ^2+12*r1^3*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*ΔQ^2*Δθ^4+r1^6*Δθ^6+Δr^4*((12*r1^3*(a^2+r1*(-2*M+r1+r1*ur1^2))*(a^4*(2*M+r1)+a^2*r1*(l1^2-4*M^2+2*M*r1*ur1^2+r1^2*(2+ur1^2))+r1^2*(r1^2*(-2*M+r1+r1*ur1^2)+l1^2*(-2*M+r1+5*r1*ur1^2)))*ΔQ^2)/(a^2+r1*(-2*M+r1))^4+(3*r1^6*(a^2+r1*(-2*M+r1+r1*ur1^2))^2*Δθ^2)/(a^2+r1*(-2*M+r1))^4)+Δr^3*((16*l1*r1^3*ur1*(2*l1^2*r1^3*ur1^2+3*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*(a^2+r1*(-2*M+r1+r1*ur1^2)))*ΔQ^2*ΔR)/(a^2+r1*(-2*M+r1))^3+(12*l1*r1^6*ur1*(a^2+r1*(-2*M+r1+r1*ur1^2))*ΔR*Δθ^2)/(a^2+r1*(-2*M+r1))^3)+Δr^2*((48*r1^2*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*(4*l1^2*r1^2*ur1^2+(l1^2+r1^2+(a^2*(2*M+r1))/r1)*(a^2+r1*(-2*M+r1+r1*ur1^2)))*ΔQ^4)/(a^2+r1*(-2*M+r1))^2+(24*r1^3*(2*l1^2*r1^3*ur1^2+(a^2*(2*M+r1)+r1*(l1^2+r1^2))*(a^2+r1*(-2*M+r1+r1*ur1^2)))*ΔQ^2*Δθ^2)/(a^2+r1*(-2*M+r1))^2+(3*r1^6*(a^2+r1*(-2*M+r1+r1*ur1^2))*Δθ^4)/(a^2+r1*(-2*M+r1))^2)+Δr*((96*l1*(a^2*(2*M+r1)+r1*(l1^2+r1^2))^2*ur1*ΔQ^4*ΔR)/(a^2+r1*(-2*M+r1))+(48*l1*r1^3*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*ur1*ΔQ^2*ΔR*Δθ^2)/(a^2+r1*(-2*M+r1))+(6*l1*r1^6*ur1*ΔR*Δθ^4)/(a^2-2*M*r1+r1^2)))/(4*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*ΔQ^2+(r1^2*(a^2+r1*(-2*M+r1+r1*ur1^2))*Δr^2)/(a^2+r1*(-2*M+r1))^2+(2*l1*r1^2*ur1*Δr*ΔR)/(a^2-2*M*r1+r1^2)+r1^2*Δθ^2)^(7/2)+(-(r1^5*(a^2-M*r1)*(a^2+r1*(-2*M+r1+r1*ur1^2))^3*Δr^7)/(2*(a^2+r1*(-2*M+r1))^7)+(32*l1*(-(a^2*M)+r1^3)*(a^2*(2*M+r1)+r1*(l1^2+r1^2))^2*ur1*ΔQ^6*ΔR)/r1^4-(r1^4*(2*a^3*e1*M+6*a*e1*M*r1^2+l1*r1^2*(-9*M+2*r1)+a^2*l1*(-2*M+5*r1))*ur1*(a^2+r1*(-2*M+r1+r1*ur1^2))^2*Δr^6*ΔR)/(2*(a^2+r1*(-2*M+r1))^6)+8*l1*(a^2+l1^2+3*r1^2)*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*ur1*ΔQ^4*ΔR*Δθ^2+2*l1*r1^2*(2*l1^2*r1+3*r1^3+a^2*(3*M+2*r1))*ur1*ΔQ^2*ΔR*Δθ^4+(l1*r1^5*ur1*ΔR*Δθ^6)/2+Δr^5*((-2*r1^2*(a^2+r1*(-2*M+r1+r1*ur1^2))*(2*a^5*e1*l1*M+a^6*(3*M+2*r1)+6*a*e1*l1*M*r1^3*(-2*M+r1+5*r1*ur1^2)+2*a^3*e1*l1*M*r1*(-2*M+r1*(4+5*ur1^2))+a^4*(-2*l1^2*(M-r1)+r1*(-8*M^2+4*M*r1*(-1+ur1^2)+r1^2*(5+2*ur1^2)))+r1^3*(2*l1^2*(3*M-r1)*(2*M-r1*(1+5*ur1^2))+r1^2*(8*M^2-2*M*r1*(3+ur1^2)-r1^2*(-1+ur1^4)))+a^2*r1*(2*l1^2*(2*M^2+r1^2*(2+5*ur1^2)-M*r1*(6+5*ur1^2))+r1*(4*M^3-4*M^2*r1*(-1+ur1^2)+2*r1^3*(2+ur1^2)+M*r1^2*(-13-2*ur1^2+ur1^4))))*ΔQ^2)/(a^2+r1*(-2*M+r1))^5+(r1^5*(a^2+r1*(-2*M+r1+r1*ur1^2))^2*(-3*a^2+r1*(4*M+r1*(-1+ur1^2)))*Δθ^2)/(2*(a^2+r1*(-2*M+r1))^5))+Δr^4*((-2*r1*ur1*(4*a^7*e1*M*(2*M+r1)+a^6*l1*(-8*M^2+5*M*r1+6*r1^2)+4*a^5*e1*M*r1*(3*l1^2-4*M^2+2*M*r1*(3+ur1^2)+r1^2*(5+ur1^2))+a^4*l1*r1*(16*M^3+6*l1^2*(-2*M+r1)+10*M*r1^2*(-2+ur1^2)-8*M^2*r1*(5+ur1^2)+r1^3*(19+6*ur1^2))-12*a*e1*M*r1^4*(-(r1^2*(-2*M+r1+r1*ur1^2))+l1^2*(6*M-r1*(3+5*ur1^2)))-4*a^3*e1*M*r1^2*(r1*(12*M^2+M*r1*(2-6*ur1^2)-r1^2*(7+4*ur1^2))+l1^2*(6*M-r1*(12+5*ur1^2)))+l1*r1^4*(2*l1^2*(5*M-2*r1)*(6*M-r1*(3+5*ur1^2))+r1^2*(40*M^2-2*M*r1*(17+5*ur1^2)+r1^2*(7+2*ur1^2-5*ur1^4)))+a^2*l1*r1^2*(2*l1^2*(12*M^2+r1^2*(9+5*ur1^2)-M*r1*(27+10*ur1^2))+r1*(44*M^3+4*M^2*r1*(1-8*ur1^2)+4*r1^3*(5+2*ur1^2)+M*r1^2*(-59-8*ur1^2+5*ur1^4))))*ΔQ^2*ΔR)/(a^2+r1*(-2*M+r1))^4+(r1^4*ur1*(a^2+r1*(-2*M+r1+r1*ur1^2))*(-4*a^3*e1*M+a^2*l1*(4*M-9*r1)-12*a*e1*M*r1^2+l1*r1^2*(20*M+r1*(-7+5*ur1^2)))*ΔR*Δθ^2)/(2*(a^2+r1*(-2*M+r1))^4))+Δr^3*((8*(-4*l1*r1*(2*a^3*e1*M+6*a*e1*M*r1^2+a^2*l1*(-2*M+r1)+l1*r1^2*(-5*M+2*r1))*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*ur1^2-r1*(a^2-M*r1)*(l1^2+r1^2+(a^2*(2*M+r1))/r1)^2*(a^2+r1*(-2*M+r1+r1*ur1^2))+4*l1^2*r1^2*(-(a^2*M)+r1^3)*ur1^2*(a^2+r1*(-2*M+r1+r1*ur1^2))-4*l1^2*r1^2*(a^2+r1*(-2*M+r1))*ur1^2*(-(a^2*M)+r1^3+(2*a^3*e1*l1*M+6*a*e1*l1*M*r1^2+a^2*(-2*l1^2*M+M*r1^2*ur1^2)-r1^2*(l1^2*(4*M-2*r1)+r1^3*ur1^2))/(a^2+r1*(-2*M+r1)))+(2*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*(a^2+r1*(-2*M+r1+r1*ur1^2))*(a^4*M-2*a^3*e1*l1*M-6*a*e1*l1*M*r1^2+r1^2*(l1^2*(4*M-2*r1)+r1^2*(2*M+r1*(-1+ur1^2)))+a^2*(2*l1^2*M-r1*(2*M^2+r1^2+M*r1*(-1+ur1^2)))))/r1)*ΔQ^4)/(a^2+r1*(-2*M+r1))^3-(4*r1^2*(2*a^5*e1*l1*M+a^6*(3*M+2*r1)+6*a*e1*l1*M*r1^3*(-2*M+r1+3*r1*ur1^2)+2*a^3*e1*l1*M*r1*(-2*M+r1*(4+3*ur1^2))+a^4*(-2*l1^2*(M-r1)+r1*(-10*M^2+r1^2*(6+ur1^2)+M*r1*(-3+2*ur1^2)))-a^2*r1*(l1^2*(-4*M^2-r1^2*(5+3*ur1^2)+M*r1*(13+6*ur1^2))+r1*(-8*M^3+2*M^2*r1*ur1^2+r1^3*(-6-ur1^2+ur1^4)+M*r1^2*(15+ur1^2+ur1^4)))-r1^3*(r1^2*(-10*M^2+M*r1*(9+ur1^2)+2*r1^2*(-1+ur1^4))+l1^2*(-14*M^2+M*r1*(13+15*ur1^2)+r1^2*(-3-6*ur1^2+5*ur1^4))))*ΔQ^2*Δθ^2)/(a^2+r1*(-2*M+r1))^3+(r1^5*(a^2+r1*(-2*M+r1+r1*ur1^2))*(-3*a^2+r1*(5*M+2*r1*(-1+ur1^2)))*Δθ^4)/(2*(a^2+r1*(-2*M+r1))^3))+Δr^2*((8*ur1*(-((l1^2+r1^2+(a^2*(2*M+r1))/r1)^2*(2*a^3*e1*M+6*a*e1*M*r1^2+a^2*l1*(-2*M+r1)+l1*r1^2*(-5*M+2*r1)))+4*l1^3*r1^2*(-(a^2*M)+r1^3)*ur1^2+2*l1*(-(a^2*M)+r1^3)*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*(a^2+r1*(-2*M+r1+r1*ur1^2))+(4*l1*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*(a^4*M-2*a^3*e1*l1*M-6*a*e1*l1*M*r1^2+r1^2*(l1^2*(4*M-2*r1)+r1^2*(2*M+r1*(-1+ur1^2)))+a^2*(2*l1^2*M-r1*(2*M^2+r1^2+M*r1*(-1+ur1^2)))))/r1)*ΔQ^4*ΔR)/(a^2+r1*(-2*M+r1))^2-(4*r1*ur1*(2*a^5*e1*M*(2*M+r1)+6*a*e1*M*r1^3*(3*l1^2+r1^2)+a^4*l1*(-4*M^2+M*r1+2*r1^2)+2*a^3*e1*M*r1*(3*l1^2+6*M*r1+4*r1^2)-l1*r1^3*(l1^2*(15*M-7*r1+5*r1*ur1^2)+r1^2*(9*M-4*r1+6*r1*ur1^2))-a^2*l1*r1*(l1^2*(6*M-2*r1)+r1*(12*M^2+3*r1^2*(-2+ur1^2)+M*r1*(4+3*ur1^2))))*ΔQ^2*ΔR*Δθ^2)/(a^2+r1*(-2*M+r1))^2+(r1^4*ur1*(-2*a^3*e1*M+a^2*l1*(2*M-3*r1)-6*a*e1*M*r1^2+l1*r1^2*(9*M-4*r1+6*r1*ur1^2))*ΔR*Δθ^4)/(2*(a^2+r1*(-2*M+r1))^2))+Δr*(32*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*((4*l1^2*(-(a^2*M)+r1^3)*ur1^2)/(a^2+r1*(-2*M+r1))-((l1^2+r1^2+(a^2*(2*M+r1))/r1)*(-(a^2*M)+r1^3+(2*a^3*e1*l1*M+6*a*e1*l1*M*r1^2+a^2*(-2*l1^2*M+M*r1^2*ur1^2)-r1^2*(l1^2*(4*M-2*r1)+r1^3*ur1^2))/(a^2+r1*(-2*M+r1))))/r1^2)*ΔQ^6+8*((4*l1^2*r1^2*(-(a^2*M)+r1^3)*ur1^2)/(a^2+r1*(-2*M+r1))+(4*l1^2*r1^2*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*ur1^2)/(a^2+r1*(-2*M+r1))+(l1^2+r1^2+(a^2*(2*M+r1))/r1)^2*(-r1+(r1^3*ur1^2)/(a^2-2*M*r1+r1^2))-2*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*(-(a^2*M)+r1^3+(2*a^3*e1*l1*M+6*a*e1*l1*M*r1^2+a^2*(-2*l1^2*M+M*r1^2*ur1^2)-r1^2*(l1^2*(4*M-2*r1)+r1^3*ur1^2))/(a^2+r1*(-2*M+r1))))*ΔQ^4*Δθ^2+(2*r1^2*(-2*a^3*e1*l1*M-6*a*e1*l1*M*r1^2-a^4*(3*M+2*r1)+r1^2*(l1^2*(8*M-4*r1+6*r1*ur1^2)+3*r1^2*(2*M+r1*(-1+ur1^2)))+a^2*(2*l1^2*(M-r1)+r1*(6*M^2+r1^2*(-5+2*ur1^2)+M*(r1+3*r1*ur1^2))))*ΔQ^2*Δθ^4)/(a^2+r1*(-2*M+r1))+(r1^4*(-r1+(r1^3*ur1^2)/(a^2-2*M*r1+r1^2))*Δθ^6)/2))/(4*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*ΔQ^2+(r1^2*(a^2+r1*(-2*M+r1+r1*ur1^2))*Δr^2)/(a^2+r1*(-2*M+r1))^2+(2*l1*r1^2*ur1*Δr*ΔR)/(a^2-2*M*r1+r1^2)+r1^2*Δθ^2)^(7/2)+((-32*(a^2*(2*M+r1)+r1*(l1^2+r1^2))*(-(a^8*M^2*(2*M+r1))+4*a^7*e1*l1*M^2*(2*M+r1)-12*a*e1*l1*M*r1^6*(l1^2+r1^2)+4*a^3*e1*l1*M*r1^3*(l1^2*(3*M-r1)-r1^2*(3*M+4*r1))+4*a^5*e1*l1*M*r1*(l1^2*M+r1*(6*M^2+2*M*r1-r1^2))+3*r1^6*(l1^4*(4*M-r1)+r1^4*(2*M+r1*ur1^2)-l1^2*r1^2*(-6*M+r1+2*r1*ur1^2))+3*a^2*r1^4*(4*l1^4*M+l1^2*r1*(12*M^2+10*M*r1-r1^2)+r1^3*(8*M^2+r1^2*ur1^2+M*r1*(6-4*ur1^2)))+a^4*M*r1*(-4*l1^4*M+3*r1^3*(14*M^2+M*r1*(17-19*ur1^2)+2*r1^2*(3-5*ur1^2))+l1^2*r1*(18*M^2+6*r1^2*(3-2*ur1^2)-5*M*r1*(-7+6*ur1^2)))+a^6*M*(-(l1^2*M*(8*M+5*r1))+r1*(36*M^3+M*r1^2*(26-45*ur1^2)+6*r1^3*(1-2*ur1^2)-6*M^2*r1*(-8+7*ur1^2))))*ΔQ^8)/(3*r1^8)-(r1^3*(a^2+r1*(-2*M+r1+r1*ur1^2))^2*(4*a^5*e1*l1*M+4*a*e1*l1*M*r1^3*(-2*M+r1)+8*a^3*e1*l1*M*r1*(-M+r1)-a^6*(2*e1^2*M+r1)+M*r1^4*(6*M^2+M*r1*(-7+4*e1^2-3*ur1^2)+2*r1^2*(1-e1^2+ur1^2))+a^2*r1*(2*l1^2*M*(2*M-r1)+r1^2*((-11+8*e1^2)*M^2-2*r1^2*(1+ur1^2)+2*M*r1*(5-3*e1^2+2*ur1^2)))-a^4*(2*l1^2*M+r1*(e1^2*(-4*M^2+6*M*r1)+r1*(-6*M+r1*(3+ur1^2)))))*Δr^8)/(4*(a^2+r1*(-2*M+r1))^8)+(r1^3*ur1*(5*a^9*e1*M+a^8*l1*(-5*M-2*(-2+e1^2)*r1)+a^7*e1*M*r1*(-29*M+r1*(21+10*ur1^2))+a^5*e1*M*r1^2*(24*l1^2+56*M^2-M*r1*(93+38*ur1^2)+r1^2*(31+32*ur1^2+5*ur1^4))+a^3*e1*M*r1^3*(-36*M^3+4*M^2*r1*(31+9*ur1^2)-M*r1^2*(91+84*ur1^2+9*ur1^4)+r1^3*(19+30*ur1^2+11*ur1^4)+16*l1^2*(-3*M+r1*(6+ur1^2)))+a^6*l1*r1*(2*l1^2+29*M^2-2*M*r1*(23+5*ur1^2)-2*r1^2*(-4*(3+ur1^2)+e1^2*(7+ur1^2)))+a^2*l1*r1^3*(36*M^4-4*M^3*r1*(40+9*ur1^2)+M^2*r1^2*(227+120*ur1^2+9*ur1^4)-2*M*r1^3*(89+63*ur1^2+10*ur1^4)+2*r1^4*(38+31*ur1^2+7*ur1^4-5*e1^2*(7+2*ur1^2))+2*l1^2*(2*M-r1)*(12*M-r1*(15+4*ur1^2)))+a*e1*M*r1^4*(-((11*M-4*r1)*r1*(-2*M+r1+r1*ur1^2)^2)+8*l1^2*(4*M^2-2*M*r1*(7+ur1^2)+r1^2*(19+5*ur1^2)))+a^4*l1*r1^2*(-56*M^3+M^2*r1*(145+38*ur1^2)-M*r1^2*(136+66*ur1^2+5*ur1^4)+l1^2*(-24*M+2*r1*(6+ur1^2))+2*r1^3*(28+19*ur1^2+2*ur1^4-e1^2*(21+5*ur1^2)))+l1*r1^4*(-4*l1^2*(2*M-r1)*(4*M^2-M*r1*(9+2*ur1^2)+r1^2*(10+3*ur1^2))+r1*(44*M^4+4*M^3*r1*(-26+4*e1^2-11*ur1^2)-4*r1^4*(-1+e1^2-ur1^2)*(10+3*ur1^2)+M^2*r1^2*(127+82*ur1^2+11*ur1^4-8*e1^2*(4+ur1^2))+M*r1^3*(-123-82*ur1^2-15*ur1^4+4*e1^2*(10+3*ur1^2)))))*Δr^7*ΔR)/(2*(a^2+r1*(-2*M+r1))^7)-(8*(-4*a^7*e1*l1*M*(8*M^2+10*M*r1+3*r1^2)+2*a^8*M*(10*M^2+11*M*r1+3*r1^2)-12*a*e1*l1*M*r1^4*(3*l1^4+8*l1^2*r1^2+5*r1^4)-4*a^3*e1*l1*M*r1^2*(3*l1^4+2*l1^2*r1*(15*M+13*r1)+r1^3*(42*M+29*r1))-4*a^5*e1*l1*M*r1*(2*l1^2*(5*M+3*r1)+r1*(24*M^2+44*M*r1+17*r1^2))+2*a^6*(l1^2*M*(16*M^2+31*M*r1+12*r1^2)+r1*(12*M^4-3*r1^4+M^2*r1^2*(32-57*ur1^2)+3*M*r1^3*(1-5*ur1^2)+18*M^3*r1*(2-3*ur1^2)))+a^4*r1*(10*l1^4*M*(4*M+3*r1)+6*r1^3*(14*M^3+M^2*r1*(21-19*ur1^2)+M*r1^2*(3-8*ur1^2)+r1^3*(-3+ur1^2))+l1^2*r1*(84*M^3-24*r1^3+M^2*r1*(166-39*ur1^2)-18*M*r1^2*(-2+ur1^2)))+6*a^2*r1^2*(2*l1^6*M+r1^5*(14*M^2-M*r1*(-7+ur1^2)+3*r1^2*(-1+ur1^2))-l1^2*r1^3*(-32*M^2+r1^2*(9+ur1^2)+2*M*r1*(-7+2*ur1^2))+l1^4*r1*(14*M^2-5*r1^2+M*r1*(9+2*ur1^2)))+3*r1^4*(l1^6*(8*M-4*r1)-4*l1^4*r1^2*(-7*M+r1*(3+ur1^2))+2*r1^6*(4*M+r1*(-1+2*ur1^2))+l1^2*r1^4*(28*M-r1*(10+3*ur1^2))))*ΔQ^6*Δθ^2)/(3*r1^5)-(2*(-4*a^7*e1*l1*M*(23*M+12*r1)+a^8*(59*M^2+36*M*r1+3*r1^2)-4*a^5*e1*l1*M*r1*(18*l1^2-46*M^2+44*M*r1+49*r1^2)+12*a*e1*l1*M*r1^3*(2*l1^4+10*l1^2*(2*M-r1)*r1+9*(2*M-r1)*r1^3)+4*a^3*e1*l1*M*r1^2*(12*l1^2*(3*M-4*r1)+r1*(90*M^2+29*M*r1-64*r1^2))+a^6*(l1^2*(92*M^2+96*M*r1+6*r1^2)+r1*(-172*M^3+74*M*r1^2+M^2*r1*(22-9*ur1^2)+r1^3*(-4+3*ur1^2)))+a^4*r1*(l1^4*(72*M+9*r1-6*e1^2*r1)-l1^2*(184*M^3+28*M^2*r1-8*M*r1^2*(25+3*ur1^2)+r1^3*(26+3*ur1^2))+r1*(108*M^4+6*M*r1^3*(17+2*ur1^2)+3*r1^4*(-10+7*ur1^2)+2*M^3*r1*(-62+9*ur1^2)-M^2*r1^2*(17+9*ur1^2)))+a^2*r1^2*(6*l1^6-2*l1^4*(72*M^2-60*M*r1+(2+9*e1^2)*r1^2)-2*r1^3*(36*M^3+9*M*r1^2*(-7+ur1^2)-18*r1^3*(-1+ur1^2)+2*M^2*r1*(13+9*ur1^2))-l1^2*r1*(144*M^3+16*M^2*r1*(10+3*ur1^2)-6*M*r1^2*(48+5*ur1^2)+r1^3*(73+12*ur1^2)))+r1^3*(12*l1^6*(-2*M+r1)+l1^4*r1*(-132*M^2+4*(23+3*e1^2)*M*r1+r1^2*(-13-12*e1^2+6*ur1^2))-l1^2*(2*M-r1)*r1^3*(108*M-r1*(41+9*ur1^2))-(2*M-r1)*r1^5*(36*M+r1*(-13+18*ur1^2))))*ΔQ^4*Δθ^4)/(3*r1^2*(a^2+r1*(-2*M+r1)))-(r1*(-60*a^5*e1*l1*M+24*a^3*e1*l1*M*(5*M-6*r1)*r1+6*a^6*(7*M+r1)+12*a*e1*l1*M*r1^2*(4*l1^2+7*(2*M-r1)*r1)+a^2*r1*(12*l1^4+l1^2*(-120*M^2+60*M*r1+r1^2*(28-36*e1^2+9*ur1^2))+2*r1*(36*M^3+3*M*r1^2*(11+3*ur1^2)+r1^3*(-5+9*ur1^2)-2*M^2*r1*(28+15*ur1^2)))+2*a^4*(l1^2*(30*M+9*r1-6*e1^2*r1)+r1*(-60*M^2+r1^2*(2+3*ur1^2)+M*r1*(34+15*ur1^2)))+r1^2*(24*l1^4*(-2*M+r1)-4*(2*M-r1)*r1^3*(6*M+r1*(-2+3*ur1^2))+l1^2*r1*(-72*M^2+2*M*r1*(8+12*e1^2-9*ur1^2)+r1^2*(10-24*e1^2+21*ur1^2))))*ΔQ^2*Δθ^6)/(6*(a^2+r1*(-2*M+r1)))+(r1^3*(r1*(-3*a^2+r1*(-2*M+r1-3*r1*ur1^2))+(4*M*(-3*a^4*e1^2+6*a^3*e1*l1+6*a*e1*l1*r1^2+a^2*(-3*l1^2+2*(1-3*e1^2)*r1^2)+r1^3*(-4*M+r1*(2-3*e1^2+3*ur1^2))))/(a^2+r1*(-2*M+r1)))*Δθ^8)/24+Δr^6*((r1*(-4*a^9*e1*l1*M+a^10*(4*M-(-2+e1^2)*r1)+4*a^7*e1*l1*M*r1*(8*M+r1*(3+16*ur1^2))+4*a^5*e1*l1*M*r1^2*(12*l1^2-20*M^2-M*r1*(6+59*ur1^2)+r1^2*(29+49*ur1^2+17*ur1^4))-4*a^3*e1*l1*M*r1^3*(-16*M^3-6*M^2*r1*(2+9*ur1^2)-r1^3*(91+29*ur1^2+31*ur1^4)+M*r1^2*(52+128*ur1^2+31*ur1^4)+24*l1^2*(M-r1*(2+ur1^2)))+4*a*e1*l1*M*r1^4*(4*l1^2*(4*M^2-2*M*r1*(7+3*ur1^2)+r1^2*(19+15*ur1^2))-r1*(16*M^3-6*M^2*r1*(6+11*ur1^2)+r1^3*(-145+28*ur1^2+2*ur1^4)+M*r1^2*(104+39*ur1^2+29*ur1^4)))+a^8*(l1^2*(4*M+6*r1-4*e1^2*r1)+r1*(-36*M^2+2*M*r1*(5+14*ur1^2)+r1^2*(27+2*ur1^2+e1^2*(-12+ur1^2))))+a^6*r1*(4*l1^4-l1^2*(32*M^2+16*M*r1*(3+4*ur1^2)+r1^2*(-57-28*ur1^2+4*e1^2*(7+3*ur1^2)))+r1*(106*M^3-M^2*r1*(99+160*ur1^2)+4*M*r1^2*(-31+25*ur1^2+11*ur1^4)+r1^3*(99+25*ur1^2-2*ur1^4+2*e1^2*(-30+5*ur1^2+ur1^4))))+a^4*r1^2*(12*l1^4*(-4*M+r1*(2+ur1^2))+l1^2*(80*M^3+M^2*r1*(121+236*ur1^2)-2*M*r1^2*(168+151*ur1^2+34*ur1^4)+2*r1^3*(81+78*ur1^2+11*ur1^4-6*e1^2*(7+5*ur1^2)))+r1*(-120*M^4+92*M^3*r1*(2+3*ur1^2)+M^2*r1^2*(243-366*ur1^2-148*ur1^4)+2*M*r1^3*(-209+18*ur1^2+61*ur1^4+10*ur1^6)+r1^4*(201+56*ur1^2-20*ur1^4-2*ur1^6+e1^2*(-164+39*ur1^2+16*ur1^4))))+r1^4*(-8*l1^4*(2*M-r1)*(4*M^2-3*M*r1*(3+2*ur1^2)+r1^2*(10+9*ur1^2))+l1^2*r1*(116*M^4+2*M^3*r1*(-170+16*e1^2-97*ur1^2)+M^2*r1^2*(569+313*ur1^2+68*ur1^4-16*e1^2*(4+3*ur1^2))+r1^4*(231+110*ur1^2+50*ur1^4-8*e1^2*(10+9*ur1^2))+4*M*r1^3*(-169-56*ur1^2-13*ur1^4+2*e1^2*(10+9*ur1^2)))+r1^3*(148*M^4+4*M^3*r1*(-89+18*e1^2-ur1^2)+M^2*r1^2*(465+34*ur1^2-107*ur1^4+12*e1^2*(-11+3*ur1^2))-2*M*r1^3*(236+21*ur1^2-62*ur1^4-18*ur1^6+e1^2*(-79+24*ur1^2+18*ur1^4))+r1^4*(155+113*ur1^2-68*ur1^4-26*ur1^6+e1^2*(-155+46*ur1^2+30*ur1^4))))+a^2*r1^3*(12*l1^4*(2*M-r1)*(4*M-r1*(5+4*ur1^2))-l1^2*(64*M^4+4*M^3*r1*(41+54*ur1^2)+2*M*r1^3*(328+263*ur1^2+78*ur1^4)-M^2*r1^2*(566+573*ur1^2+124*ur1^4)+r1^4*(-263-222*ur1^2-86*ur1^4+20*e1^2*(7+6*ur1^2)))+r1*(40*M^5-4*M^4*r1*(21+34*ur1^2)+2*M^3*r1^2*(-147+144*ur1^2+53*ur1^4)+2*M*r1^4*(-301-30*ur1^2+79*ur1^4+16*ur1^6)-M^2*r1^3*(-639+116*ur1^2+187*ur1^4+24*ur1^6)+r1^5*(282+67*ur1^2-62*ur1^4-18*ur1^6+e1^2*(-270+76*ur1^2+44*ur1^4)))))*ΔQ^2)/(2*(a^2+r1*(-2*M+r1))^6)+(r1^4*(a^8*(9-4*e1^2)+48*a^5*e1*l1*M*r1-32*a^3*e1*l1*M*r1^2*(3*M-r1*(6+ur1^2))+16*a*e1*l1*M*r1^3*(4*M^2-2*M*r1*(7+ur1^2)+r1^2*(19+5*ur1^2))+2*a^6*(2*l1^2+r1*(-33*M+r1*(25+7*ur1^2-2*e1^2*(7+ur1^2))))+2*a^2*r1^2*(2*l1^2*(2*M-r1)*(12*M-r1*(15+4*ur1^2))-r1*(94*M^3-3*M^2*r1*(63+23*ur1^2)+M*r1^2*(171+114*ur1^2+7*ur1^4)+2*r1^3*(-38-32*ur1^2-7*ur1^4+ur1^6+5*e1^2*(7+2*ur1^2))))+a^4*r1*(l1^2*(-48*M+4*r1*(6+ur1^2))+r1*(173*M^2-4*M*r1*(61+20*ur1^2)+r1^2*(113+74*ur1^2+ur1^4-4*e1^2*(21+5*ur1^2))))+r1^3*(-8*l1^2*(2*M-r1)*(4*M^2-M*r1*(9+2*ur1^2)+r1^2*(10+3*ur1^2))+r1*(68*M^4+4*M^3*r1*(-45+8*e1^2-17*ur1^2)+M^2*r1^2*(241+162*ur1^2+17*ur1^4-16*e1^2*(4+ur1^2))+4*r1^4*(20+27*ur1^2+8*ur1^4+ur1^6-2*e1^2*(10+3*ur1^2))+4*M*r1^3*(-61-44*ur1^2-11*ur1^4+e1^2*(20+6*ur1^2)))))*Δθ^2)/(8*(a^2+r1*(-2*M+r1))^6))+Δr^5*((ur1*(2*a^9*e1*M*(41*M+27*r1)+a^8*l1*(-82*M^2-18*M*r1+3*e1^2*r1^2)+2*a^7*e1*M*r1*(6*l1^2-170*M^2+2*M*r1*(-10+29*ur1^2)+r1^2*(118+33*ur1^2))+2*a^5*e1*M*r1^2*(176*M^3-2*M^2*r1*(49+61*ur1^2)+6*l1^2*(-2*M+r1+9*r1*ur1^2)+2*r1^3*(112+52*ur1^2+3*ur1^4)+M*r1^2*(-302+25*ur1^2+17*ur1^4))-2*a^6*l1*r1*(-170*M^3+6*l1^2*(M+(-1+e1^2)*r1)+3*M*r1^2*(9-16*ur1^2)+M^2*r1*(67+58*ur1^2)-3*r1^3*(2-2*ur1^2+e1^2*(5+2*ur1^2)))+a^4*l1*r1^2*(12*l1^4-352*M^4+2*M^3*r1*(191+122*ur1^2)+M^2*r1^2*(53-536*ur1^2-34*ur1^4)+6*M*r1^3*(-24+49*ur1^2+19*ur1^4)+6*l1^2*(4*M^2+2*r1^2*(8-5*e1^2+ur1^2)-M*r1*(13+18*ur1^2))+3*r1^4*(e1^2*(39+32*ur1^2)-4*(1+9*ur1^2+ur1^4)))-6*a*e1*M*r1^4*(8*l1^4*(2*M-5*r1)+2*l1^2*r1^2*(3*M*(-6+ur1^2)+8*r1*(5+3*ur1^2))+r1^3*(-86*M^2+M*r1*(89+37*ur1^2)+r1^2*(-23-20*ur1^2+3*ur1^4)))+2*a^3*e1*M*r1^3*(48*l1^4-6*l1^2*r1*(r1*(16-7*ur1^2)+M*(2+17*ur1^2))+r1*(48*M^3+M^2*r1*(202-78*ur1^2)+r1^3*(202+131*ur1^2+7*ur1^4)+M*r1^2*(-508-100*ur1^2+27*ur1^4)))-3*a^2*l1*r1^3*(16*l1^4*(2*M-r1)+l1^2*r1*(2*r1^2*(-17+20*e1^2-6*ur1^2)+2*M*r1*(29+16*ur1^2)-M^2*(33+68*ur1^2))+r1*(20*M^4+2*M^3*r1*(18-67*ur1^2)-2*M*r1^3*(-7+91*ur1^2+32*ur1^4)+M^2*r1^2*(-92+167*ur1^2+62*ur1^4)+2*r1^4*(22+49*ur1^2+18*ur1^4-2*e1^2*(19+22*ur1^2))))+3*l1*r1^4*(8*l1^4*(4*M^2-8*M*r1+3*r1^2)+l1^2*r1*(-2*M^3+M^2*r1*(1-16*e1^2-24*ur1^2)-2*r1^3*(9+12*e1^2+10*ur1^2)+4*M*r1^2*(9+6*e1^2+19*ur1^2))+r1^3*(-26*M^3+M^2*r1*(17+36*e1^2-135*ur1^2)+2*M*r1^2*(35+90*ur1^2+37*ur1^4-12*e1^2*(2+3*ur1^2))+2*r1^3*(e1^2*(23+30*ur1^2)-9*(2+5*ur1^2+3*ur1^4)))))*ΔQ^2*ΔR)/(3*(a^2+r1*(-2*M+r1))^5)+(r1^3*ur1*(24*a^7*e1*M+a^6*l1*(-24*M+(7-4*e1^2)*r1)+2*a^5*e1*M*r1*(-49*M+r1*(45+11*ur1^2))+a^4*l1*r1*(4*l1^2+98*M^2-r1^2*(-47+20*e1^2+ur1^2)-2*M*r1*(57+11*ur1^2))+2*a^3*e1*M*r1^2*(16*l1^2+50*M^2-M*r1*(134+23*ur1^2)+r1^2*(56+29*ur1^2-ur1^4))+a^2*l1*r1^2*(-100*M^3+16*l1^2*(-2*M+r1)+M^2*r1*(267+46*ur1^2)+4*r1^3*(19-10*e1^2+10*ur1^2-2*ur1^4)+2*M*r1^2*(-117-28*ur1^2+ur1^4))+l1*r1^3*(8*l1^2*(4*M^2-8*M*r1+3*r1^2)+r1*(-130*M^3+M^2*r1*(221-16*e1^2+61*ur1^2)+2*M*r1^2*(-75+12*e1^2-46*ur1^2+ur1^4)+4*r1^3*(9-6*e1^2+11*ur1^2+2*ur1^4)))-2*a*e1*M*r1^3*(8*l1^2*(2*M-5*r1)+r1*(-86*M^2+M*r1*(89+37*ur1^2)+r1^2*(-23-20*ur1^2+3*ur1^4))))*ΔR*Δθ^2)/(4*(a^2+r1*(-2*M+r1))^5))+Δr^4*((2*(-4*a^11*e1*l1*M*(4*M+3*r1)-a^12*(14*M^2+6*M*r1+3*r1^2)+4*a^9*e1*l1*M*r1*(-12*l1^2+30*M^2+3*M*r1*(5+29*ur1^2)+2*r1^2*(-7+30*ur1^2))+4*a^7*e1*l1*M*r1^2*(-72*M^3-6*M^2*r1*(3+62*ur1^2)+3*r1^3*(-12+87*ur1^2+8*ur1^4)+M*r1^2*(72-81*ur1^2+67*ur1^4)+l1^2*(75*M+6*r1*(-10+ur1^2)))+4*a^5*e1*l1*M*r1^3*(18*l1^4+56*M^4+12*M^3*(r1+33*r1*ur1^2)+r1^4*(-54+513*ur1^2+53*ur1^4)-2*M^2*r1^2*(57+60*ur1^2+67*ur1^4)+M*r1^3*(146-711*ur1^2+124*ur1^4)-3*l1^2*(52*M^2+M*r1*(-87+10*ur1^2)+4*r1^2*(14+11*ur1^2)))+a^10*(l1^2*(16*M^2+24*M*r1+3*(-3+e1^2)*r1^2)+r1*(12*M^3-3*r1^3*(-2+ur1^2)+6*M*r1^2*(9+14*ur1^2)+2*M^2*r1*(-45+79*ur1^2)))+12*a*e1*l1*M*r1^5*(l1^4*(8*M^2-28*M*r1+38*r1^2)+l1^2*r1*(44*M^3-4*M^2*r1*(24+23*ur1^2)+M*r1^2*(143+230*ur1^2)-r1^3*(153+464*ur1^2))+(2*M-r1)*r1^3*(10*M^2+M*r1*(-13+102*ur1^2)+r1^2*(4-57*ur1^2+11*ur1^4)))-4*a^3*e1*l1*M*r1^4*(36*l1^4*(M-2*r1)-3*l1^2*(36*M^3+12*M^2*r1*(-10+ur1^2)-6*r1^3*(19+37*ur1^2)+M*r1^2*(139+108*ur1^2))+r1*(24*M^4-4*M^3*r1*(16+9*ur1^2)+M*r1^3*(-156+1191*ur1^2-47*ur1^4)+r1^4*(41-483*ur1^2+4*ur1^4)+6*M^2*r1^2*(29-84*ur1^2+35*ur1^4)))+a^8*r1*(6*l1^4*(8*M-e1^2*r1)+r1*(204*M^4+M^3*r1*(444-980*ur1^2)+3*r1^4*(21+ur1^2)+6*M*r1^3*(16+68*ur1^2+17*ur1^4)+M^2*r1^2*(-759-98*ur1^2+202*ur1^4))-6*l1^2*(20*M^3-M*r1^2*(41+5*ur1^2)+M^2*r1*(33+58*ur1^2)+2*r1^3*(1+3*ur1^2-3*e1^2*(1+ur1^2))))+a^6*r1^2*(6*l1^6-3*l1^4*(100*M^2+8*M*r1*(-8+ur1^2)+r1^2*(-9+14*e1^2+8*ur1^2))+r1*(-512*M^5+4*M^4*r1*(-156+491*ur1^2)+3*r1^5*(44+13*ur1^2-2*ur1^4)-4*M^3*r1^2*(-672+155*ur1^2+185*ur1^4)+6*M*r1^4*(-30+107*ur1^2+48*ur1^4+2*ur1^6)+M^2*r1^3*(-1316-1609*ur1^2+10*ur1^4+30*ur1^6))+l1^2*(288*M^4+48*M^3*r1*(12+31*ur1^2)+6*M*r1^3*(74+31*ur1^2+52*ur1^4)-2*M^2*r1^2*(618+495*ur1^2+134*ur1^4)+3*r1^4*(-19-135*ur1^2-12*ur1^4+60*e1^2*(1+2*ur1^2))))+a^4*r1^3*(36*l1^6*(-2*M+r1)+3*l1^4*(208*M^3+12*M*r1^2*(8+13*ur1^2)+M^2*r1*(-277+40*ur1^2)-2*r1^3*(-6+21*e1^2+41*ur1^2))+3*r1*(112*M^6+8*M^5*r1*(12-53*ur1^2)+r1^6*(41+23*ur1^2-ur1^4)+4*M^4*r1^2*(-296+75*ur1^2+56*ur1^4)+M^2*r1^4*(-124-725*ur1^2-178*ur1^4+2*ur1^6)+2*M*r1^5*(-81+56*ur1^2+53*ur1^4+2*ur1^6)-2*M^3*r1^3*(-556-395*ur1^2+60*ur1^4+10*ur1^6))+l1^2*(-224*M^5-792*M^4*(r1+2*r1*ur1^2)+6*M*r1^4*(95+282*ur1^2+158*ur1^4)+2*M^3*r1^2*(1092+1131*ur1^2+268*ur1^4)-M^2*r1^3*(1568+873*ur1^2+1660*ur1^4)+3*r1^5*(-109-494*ur1^2-132*ur1^4+4*e1^2*(41+117*ur1^2))))+3*a^2*r1^4*(6*l1^6*(8*M^2-14*M*r1+5*r1^2)-l1^4*(144*M^4+4*M^3*r1*(-89+12*ur1^2)-8*M*r1^3*(23+99*ur1^2)+2*M^2*r1^2*(145+213*ur1^2)+r1^4*(29+70*e1^2+270*ur1^2))+r1^3*(512*M^5-8*M^4*r1*(98+61*ur1^2)+M^2*r1^3*(178-247*ur1^2-138*ur1^4)+2*M*r1^4*(-59-7*ur1^2+20*ur1^4)+4*M^3*r1^2*(59+164*ur1^2+29*ur1^4)+2*r1^5*(9+8*ur1^2+2*ur1^4+ur1^6))+l1^2*r1*(160*M^5-12*M^4*r1*(36+17*ur1^2)+8*M^3*r1^2*(63+23*ur1^2+64*ur1^4)-4*M^2*r1^3*(91+214*ur1^2+158*ur1^4)+2*M*r1^4*(191+721*ur1^2+316*ur1^4)+r1^5*(-241-965*ur1^2-399*ur1^4+6*e1^2*(45+152*ur1^2))))-3*r1^5*(4*l1^6*(8*M^3-22*M^2*r1+29*M*r1^2-10*r1^3)+l1^4*r1*(100*M^4-4*M^3*r1*(49+4*e1^2+101*ur1^2)-8*M*r1^3*(40+5*e1^2+166*ur1^2)+r1^4*(111+40*e1^2+464*ur1^2)+M^2*r1^2*(269+32*e1^2+898*ur1^2))-(2*M-r1)*r1^5*(30*M^3-M^2*r1*(47+3*ur1^2)-2*M*r1^2*(-11-6*ur1^2+ur1^4)-r1^3*(3+4*ur1^2+3*ur1^4+2*ur1^6))+l1^2*r1^3*(72*M^4+6*M^3*r1*(-28+12*e1^2-77*ur1^2)+M^2*r1^2*(314+1083*ur1^2+456*ur1^4-12*e1^2*(11+36*ur1^2))+2*M*r1^3*(-212-786*ur1^2-309*ur1^4+e1^2*(79+288*ur1^2))+r1^4*(150+673*ur1^2+567*ur1^4-e1^2*(155+552*ur1^2)))))*ΔQ^4)/(3*r1^2*(a^2+r1*(-2*M+r1))^5)+(r1*(12*a^9*e1*l1*M-2*a^10*(3*M+(-1+e1^2)*r1)+4*a^7*e1*l1*M*r1*(-17*M+r1*(31+24*ur1^2))+4*a^5*e1*l1*M*r1^2*(12*l1^2+32*M^2-M*r1*(141+100*ur1^2)+r1^2*(109+90*ur1^2-3*ur1^4))-4*a^3*e1*l1*M*r1^3*(20*M^3+24*l1^2*(M-2*r1)-4*M^2*r1*(57+26*ur1^2)+M*r1^2*(287+278*ur1^2-6*ur1^4)+r1^3*(-229-105*ur1^2+12*ur1^4))+4*a*e1*l1*M*r1^4*(4*l1^2*(4*M^2-14*M*r1+19*r1^2)+r1*(-124*M^3+4*M^2*r1*(57+46*ur1^2)+3*r1^3*(102+5*ur1^2-3*ur1^4)+M*r1^2*(-295-184*ur1^2+18*ur1^4)))+a^8*(-2*l1^2*(6*M+(-3+2*e1^2)*r1)+r1*(34*M^2+6*M*r1*(-6+5*ur1^2)+r1^2*(44-ur1^2+e1^2*(-24+ur1^2))))+a^6*r1*(4*l1^4+2*l1^2*(34*M^2+r1^2*(40-14*e1^2-5*ur1^2)-M*r1*(71+48*ur1^2))+r1*(-80*M^3-4*M^2*r1*(-39+50*ur1^2)+4*M*r1^2*(-83+27*ur1^2+8*ur1^4)+r1^3*(188+20*ur1^2-3*ur1^4+10*e1^2*(-12+ur1^2))))+r1^4*(-8*l1^4*(8*M^3-22*M^2*r1+29*M*r1^2-10*r1^3)+l1^2*r1*(424*M^4+2*M^3*r1*(-512+16*e1^2-233*ur1^2)+2*M*r1^3*(-619+40*e1^2-199*ur1^2-24*ur1^4)+M^2*r1^2*(1290-64*e1^2+781*ur1^2-16*ur1^4)+2*r1^4*(199-40*e1^2+57*ur1^2+14*ur1^4))+2*r1^3*(204*M^4+6*M^3*r1*(-78+12*e1^2-7*ur1^2)+M^2*r1^2*(551+101*ur1^2-22*ur1^4+6*e1^2*(-22+3*ur1^2))-2*M*r1^3*(251+58*ur1^2-9*ur1^4+2*ur1^6+e1^2*(-79+12*ur1^2))+r1^4*(159+138*ur1^2-19*ur1^4+2*ur1^6+e1^2*(-155+23*ur1^2))))+a^2*r1^3*(12*l1^4*(8*M^2-14*M*r1+5*r1^2)+l1^2*(80*M^4-16*M^3*r1*(53+26*ur1^2)+M^2*r1^2*(1480+845*ur1^2-24*ur1^4)+4*r1^4*(104-35*e1^2+45*ur1^2+ur1^4)+2*M*r1^3*(-633-309*ur1^2+34*ur1^4))-2*r1*(32*M^5+28*M^4*r1*(-4+5*ur1^2)-2*M^3*r1^2*(-276+104*ur1^2+35*ur1^4)+M^2*r1^3*(-822+28*ur1^2+81*ur1^4-4*ur1^6)+M*r1^4*(669+104*ur1^2-45*ur1^4+2*ur1^6)-r1^5*(292+95*ur1^2-13*ur1^4+2*ur1^6+e1^2*(-270+38*ur1^2))))+a^4*r1^2*(24*l1^4*(-2*M+r1)-2*l1^2*(64*M^3-5*M^2*r1*(57+40*ur1^2)+M*r1^2*(343+138*ur1^2-6*ur1^4)+r1^3*(-125+42*e1^2-36*ur1^2+12*ur1^4))+r1*(104*M^4+4*M^3*r1*(-74+105*ur1^2)-2*M^2*r1^2*(-464+215*ur1^2+67*ur1^4)+2*M*r1^3*(-476+9*ur1^2+42*ur1^4-2*ur1^6)+r1^4*(412+93*ur1^2-15*ur1^4+e1^2*(-328+39*ur1^2)))))*ΔQ^2*Δθ^2)/(2*(a^2+r1*(-2*M+r1))^5)+(r1^4*(9*a^8-96*a^3*e1*l1*M*r1^3*ur1^2+24*a*e1*l1*M*r1^4*ur1^2*(4*M-r1*(10+ur1^2))+a^6*r1*(-84*M+r1*(52+3*(-11+4*e1^2)*ur1^2))+a^4*r1^2*(273*M^2-12*l1^2*ur1^2+6*M*r1*(-53+24*ur1^2)+r1^2*(87+(-73+60*e1^2)*ur1^2+6*(-7+e1^2)*ur1^4))+a^2*r1^3*(-372*M^3+3*M^2*r1*(206-65*ur1^2)+2*M*(48*l1^2*ur1^2+r1^2*(-162+95*ur1^2+63*ur1^4))+2*r1*(-3*l1^2*ur1^2*(8+ur1^2)+r1^2*(27+(-49+60*e1^2)*ur1^2+(-40+9*e1^2)*ur1^4)))+r1^4*(180*M^4+2*M^3*r1*(-190+39*ur1^2)+M^2*(-96*l1^2*ur1^2+r1^2*(285+(-103+48*e1^2)*ur1^2-84*ur1^4))-2*M*r1*(-12*l1^2*ur1^2*(8+ur1^2)+r1^2*(45+(-74+36*e1^2)*ur1^2+(-47+6*e1^2)*ur1^4))-2*r1^2*(6*l1^2*ur1^2*(6+ur1^2)+r1^2*(-5+(29-36*e1^2)*ur1^2+(37-6*e1^2)*ur1^4+3*ur1^6))))*Δθ^4)/(24*(a^2+r1*(-2*M+r1))^5))+Δr^3*((8*ur1*(-2*a^10*l1*M*(19*M^2+12*M*r1+3*r1^2)+a^11*e1*M*(38*M^2+55*M*r1+18*r1^2)+a^9*e1*M*r1*(-176*M^3+21*l1^2*r1+r1^3*(101+12*ur1^2)+2*M^2*r1*(-111+25*ur1^2)+M*r1^2*(118+49*ur1^2))+a^8*l1*r1*(176*M^4-3*r1^2*(-2*(-1+e1^2)*l1^2+3*r1^2)+M^3*r1*(38-50*ur1^2)+2*M^2*r1^2*(-71+30*ur1^2)+3*M*r1*(l1^2+3*r1^2*(-12+5*ur1^2)))-3*a*e1*M*r1^6*(l1^4*(98*M^2-185*M*r1+316*r1^2)-(2*M-r1)*r1^4*(44*M-r1*(25+3*ur1^2))-l1^2*(2*M-r1)*r1^2*(93*M+2*r1*(-27+7*ur1^2)))+a^6*l1*r1^2*(-200*M^5+3*l1^4*(7*M-2*r1)+2*M^3*r1^2*(259-193*ur1^2)-3*r1^5*(2+ur1^2)+4*M^4*r1*(11+25*ur1^2)+12*M*r1^4*(-20+10*ur1^2+ur1^4)+M^2*r1^3*(103-121*ur1^2+30*ur1^4)+l1^2*(30*M^3+7*M^2*r1*(9-14*ur1^2)+3*r1^3*(-25+20*e1^2-2*ur1^2)+6*M*r1^2*(-3+7*ur1^2)))+a^3*e1*M*r1^4*(l1^4*(-66*M^2+426*M*r1-519*r1^2)+r1^3*(444*M^3-10*M^2*r1*(4+9*ur1^2)-M*r1^2*(617+19*ur1^2)+r1^3*(272+41*ur1^2))+l1^2*r1*(-396*M^3+6*M^2*r1*(107-50*ur1^2)+r1^3*(393+4*ur1^2)+M*r1^2*(-963+58*ur1^2)))+a^7*e1*M*r1^2*(-21*l1^4+200*M^4+2*M^2*r1^2*(-287+3*ur1^2)-4*M^3*r1*(-71+25*ur1^2)+3*M*r1^3*(6+41*ur1^2)+r1^4*(270+47*ur1^2)+l1^2*(-30*M^2+3*r1^2*(37+12*ur1^2)+M*r1*(-213+98*ur1^2)))+a^5*e1*M*r1^3*(3*l1^4*(25*M-56*r1)+r1*(-168*M^4+4*M^3*r1*(134-27*ur1^2)+r1^4*(384+67*ur1^2)-2*M^2*r1^2*(309+71*ur1^2)+M*r1^3*(-380+73*ur1^2))+l1^2*(60*M^3+2*M^2*r1*(255-98*ur1^2)+r1^3*(321+82*ur1^2)+M*r1^2*(-573+176*ur1^2)))+3*l1*r1^6*(l1^4*(86*M^3-173*M^2*r1+233*M*r1^2-84*r1^3)+l1^2*r1^2*(40*M^3+r1^3*(-79+92*e1^2-97*ur1^2)+2*M^2*r1*(-53+36*e1^2-38*ur1^2)+3*M*r1^2*(67-32*e1^2+36*ur1^2))-(2*M-r1)*r1^4*(31*M^2-M*r1*(30+ur1^2)+r1^2*(7+ur1^2+2*ur1^4)))+3*a^2*l1*r1^4*(l1^4*(22*M^3-126*M^2*r1+165*M*r1^2-54*r1^3)+l1^2*r1*(88*M^4+r1^4*(-131+152*e1^2-69*ur1^2)+2*M*r1^3*(89+51*ur1^2)+2*M^3*r1*(-65+66*ur1^2)-M^2*r1^2*(39+122*ur1^2))+r1^3*(-40*M^4+M^2*r1^2*(167-79*ur1^2)+6*M*r1^3*(-17+2*ur1^2)+2*M^3*r1*(-26+53*ur1^2)+r1^4*(18+ur1^2+2*ur1^4)))+a^4*l1*r1^3*(-3*l1^4*(25*M^2-51*M*r1+20*r1^2)+l1^2*(-60*M^4+3*r1^4*(-75+78*e1^2-22*ur1^2)+6*M*r1^3*(33+23*ur1^2)+4*M^3*r1*(-60+49*ur1^2)-4*M^2*r1^2*(-66+95*ur1^2))+r1^2*(-3*r1^4*(-12+ur1^2)+M^4*(-460+432*ur1^2)+12*M*r1^3*(-26+10*ur1^2+ur1^4)+M^2*r1^2*(449-400*ur1^2+6*ur1^4)-2*M^3*r1*(-116+17*ur1^2+30*ur1^4))))*ΔQ^4*ΔR)/(3*r1^3*(a^2+r1*(-2*M+r1))^4)+(ur1*(2*a^9*e1*M*(73*M+45*r1)-a^8*l1*(146*M^2+96*M*r1-3*(-5+e1^2)*r1^2)-a^6*l1*r1*(-632*M^3+15*l1^2*(6*M+r1)+6*M*r1^2*(47-15*ur1^2)+3*r1^3*(8-10*e1^2+3*ur1^2)+2*M^2*r1*(8+31*ur1^2))+2*a^7*e1*M*r1*(45*l1^2-316*M^2+r1^2*(227+15*ur1^2)+M*r1*(53+31*ur1^2))-2*a^5*e1*M*r1^2*(-340*M^3+M*r1^2*(445-46*ur1^2)+2*M^2*r1*(266+31*ur1^2)-r1^3*(469+50*ur1^2)+3*l1^2*(65*M+2*r1*(-30+ur1^2)))+a^4*l1*r1^2*(-680*M^4+2*M^2*r1^2*(251-286*ur1^2)+39*r1^4*(1+3*e1^2-ur1^2)+4*M^3*r1*(176+31*ur1^2)-12*M*r1^3*(42-19*ur1^2+2*ur1^4)+3*l1^2*(130*M^2+r1^2*(9-8*ur1^2)+4*M*r1*(-20+ur1^2)))+6*a*e1*M*r1^5*(2*(2*M-r1)*r1^2*(44*M-r1*(25+3*ur1^2))+l1^2*(146*M^2-6*r1^2*(5+ur1^2)+M*r1*(-137+12*ur1^2)))+2*a^3*e1*M*r1^3*(3*l1^2*(70*M^2+r1^2*(63-8*ur1^2)+2*M*r1*(-101+2*ur1^2))+r1*(444*M^3+10*M^2*r1*(8-9*ur1^2)-M*r1^2*(989+25*ur1^2)+r1^3*(437+53*ur1^2)))-6*l1*r1^5*(l1^2*(2*M-r1)*(42*M^2-M*r1*(43+2*ur1^2)+r1^2*(-5+8*ur1^2))+r1^2*(88*M^3-2*M^2*r1*(66+9*e1^2-7*ur1^2)+r1^3*(5-23*e1^2+17*ur1^2-4*ur1^4)+2*M*r1^2*(17+12*e1^2-5*ur1^2+4*ur1^4)))+6*a^2*l1*r1^3*(l1^2*(-70*M^3+M^2*r1*(139-4*ur1^2)+2*r1^3*(7+2*ur1^2)+M*r1^2*(-81+8*ur1^2))+r1*(-80*M^4+2*M^3*r1*(-2+55*ur1^2)+M*r1^3*(-111+36*ur1^2-4*ur1^4)+r1^4*(3+38*e1^2-10*ur1^2+4*ur1^4)+M^2*r1^2*(168-95*ur1^2+8*ur1^4))))*ΔQ^2*ΔR*Δθ^2)/(3*(a^2+r1*(-2*M+r1))^4)-(r1^3*ur1*(-27*a^7*e1*M+3*a^6*l1*(9*M+(5-2*e1^2)*r1)+3*a^5*e1*M*r1*(38*M-r1*(39+ur1^2))+3*a^3*e1*M*r1^2*(16*l1^2-40*M^2+2*M*r1*(62+ur1^2)-r1^2*(55+4*ur1^2))+a^4*l1*r1*(6*l1^2-114*M^2+3*M*r1*(10+ur1^2)+r1^2*(23+30*ur1^2-6*e1^2*(5+ur1^2)))+a^2*l1*r1^2*(120*M^3+M*r1^2*(85-78*ur1^2)-3*M^2*r1*(65+2*ur1^2)+6*l1^2*(-8*M+r1*(4+ur1^2))+2*r1^3*(8+25*ur1^2-3*e1^2*(10+3*ur1^2)))-3*a*e1*M*r1^3*(8*l1^2*(2*M-r1*(5+ur1^2))+(2*M-r1)*r1*(44*M-r1*(25+3*ur1^2)))+l1*r1^3*(12*l1^2*(2*M-r1)*(2*M-r1*(3+ur1^2))+r1*(138*M^3+M^2*r1*(-205-24*e1^2+42*ur1^2)+2*r1^3*(4+19*ur1^2+3*ur1^4-6*e1^2*(3+ur1^2))+M*r1^2*(52-49*ur1^2+12*e1^2*(3+ur1^2)))))*ΔR*Δθ^4)/(6*(a^2+r1*(-2*M+r1))^4))+Δr^2*((8*(-4*a^11*e1*l1*M*(22*M^2+17*M*r1+3*r1^2)+a^12*M*(22*M^2+23*M*r1+6*r1^2)-4*a^9*e1*l1*M*r1*(-76*M^3+l1^2*(29*M+6*r1)+M*r1^2*(71-96*ur1^2)+r1^3*(13-24*ur1^2)+6*M^2*r1*(7-16*ur1^2))-12*a*e1*l1*M*r1^6*(l1^4*(30*M^2-51*M*r1+80*r1^2)-l1^2*(2*M-r1)*r1^2*(28*M+r1*(-17+6*ur1^2))-(2*M-r1)*r1^4*(7*M-r1*(5+8*ur1^2)))+a^10*(l1^2*M*(88*M^2+115*M*r1+24*r1^2)-2*r1*(110*M^4+3*r1^4+M^2*r1^2*(69-91*ur1^2)+2*M^3*r1*(78-37*ur1^2)-3*M*r1^3*(-5+9*ur1^2)))-4*a^7*e1*l1*M*r1^2*(9*l1^4+l1^2*(-104*M^2+M*r1*(115-62*ur1^2)+r1^2*(13-24*ur1^2))+2*(32*M^4-52*M^2*r1^2+3*M*r1^3*(11-40*ur1^2)+3*r1^4*(1-16*ur1^2)+2*M^3*r1*(-59+48*ur1^2)))-4*a^3*e1*l1*M*r1^4*(3*l1^4*(10*M^2-46*M*r1+47*r1^2)+l1^2*r1*(276*M^3+M*r1^2*(245-22*ur1^2)+20*M^2*r1*(-13+9*ur1^2)-r1^3*(101+16*ur1^2))+r1^3*(12*M^3+M*r1^2*(77+48*ur1^2)+2*M^2*r1*(-7+96*ur1^2)-r1^3*(41+96*ur1^2)))+4*a^5*e1*l1*M*r1^3*(l1^4*(33*M-54*r1)+2*r1*(-96*M^4+2*M^3*r1*(5-48*ur1^2)-48*M^2*r1^2*(-1+3*ur1^2)+3*r1^4*(5+24*ur1^2)+M*r1^3*(-19+72*ur1^2))+l1^2*(-92*M^3-4*M^2*r1*(-95+31*ur1^2)+r1^3*(43+58*ur1^2)+M*r1^2*(-145+104*ur1^2)))+3*a^2*r1^4*(4*l1^6*(10*M^3-39*M^2*r1+45*M*r1^2-14*r1^3)+2*l1^4*r1*(116*M^4+r1^4*(-63+76*e1^2-47*ur1^2)+2*M*r1^3*(43+18*ur1^2)+4*M^3*r1*(-31+34*ur1^2)-M^2*r1^2*(11+76*ur1^2))+2*r1^5*(-92*M^4+2*M^3*r1*(32+55*ur1^2)+M^2*r1^2*(29-79*ur1^2-8*ur1^4)+r1^4*(5-5*ur1^2+ur1^4)+M*r1^3*(-29+21*ur1^2+3*ur1^4))+l1^2*r1^3*(64*M^4-22*M^2*r1^2*(-12+5*ur1^2)-2*M*r1^3*(79+27*ur1^2)+4*M^3*r1*(-44+135*ur1^2)+r1^4*(31-48*ur1^2+12*ur1^4)))+3*r1^6*(4*l1^6*(24*M^3-46*M^2*r1+59*M*r1^2-21*r1^3)+2*l1^4*r1^2*(12*M^3+r1^3*(-37+46*e1^2-61*ur1^2)+4*M^2*r1*(-9+9*e1^2-7*ur1^2)+M*r1^2*(89-48*e1^2+74*ur1^2))-(2*M-r1)*r1^6*(16*M^2+2*M*r1*(-7+3*ur1^2)+r1^2*(3-4*ur1^2+ur1^4))-l1^2*(2*M-r1)*r1^4*(52*M^2-4*M*r1*(13+6*ur1^2)+r1^2*(13-23*ur1^2+12*ur1^4)))+a^8*r1*(2*l1^4*(58*M^2+21*M*r1+3*(-1+e1^2)*r1^2)-l1^2*(304*M^4+24*r1^4+6*M*r1^3*(13-9*ur1^2)+M^2*r1^2*(-121+117*ur1^2)+2*M^3*r1*(121+192*ur1^2))+r1*(616*M^5+M^4*r1*(796-680*ur1^2)+3*r1^5*(-5+2*ur1^2)+6*M*r1^4*(-20+45*ur1^2+4*ur1^4)+6*M^3*r1^2*(-30-112*ur1^2+17*ur1^4)+M^2*r1^3*(-414+316*ur1^2+99*ur1^4)))+a^6*r1^2*(6*l1^6*(6*M-r1)+l1^4*(-416*M^3+M^2*r1*(262-248*ur1^2)+6*r1^3*(-15+10*e1^2-ur1^2)+12*M*r1^2*(5+ur1^2))+2*r1*(-264*M^6+3*r1^6*ur1^2+24*M^5*r1*(-11+16*ur1^2)+2*M^4*r1^2*(317+132*ur1^2-51*ur1^4)+3*M*r1^5*(-30+70*ur1^2+11*ur1^4)-4*M^3*r1^3*(-95+233*ur1^2+12*ur1^4)+M^2*r1^4*(-206-266*ur1^2+69*ur1^4))+l1^2*(256*M^5-3*r1^5*(11+2*ur1^2)+12*M^4*r1*(7+64*ur1^2)-4*M^3*r1^2*(53+222*ur1^2)+6*M*r1^4*(-39+11*ur1^2+12*ur1^4)+M^2*r1^3*(509-1044*ur1^2+180*ur1^4)))+a^4*r1^3*(-6*l1^6*(22*M^2-32*M*r1+11*r1^2)+l1^4*(368*M^4+6*r1^4*(-40+39*e1^2-11*ur1^2)+496*M^3*r1*(-2+ur1^2)+48*M*r1^3*(6+ur1^2)-8*M^2*r1^2*(-52+85*ur1^2))+3*r1^3*(-328*M^5+4*M^4*r1*(-5+154*ur1^2)+M^2*r1^3*(-39-368*ur1^2+ur1^4)+r1^5*(10-6*ur1^2+ur1^4)+2*M*r1^4*(-35+48*ur1^2+11*ur1^4)-2*M^3*r1^2*(-181+40*ur1^2+29*ur1^4))+l1^2*r1*(-24*M^5+9*r1^5*(5-9*ur1^2)+4*M^4*r1*(5+369*ur1^2)+12*M*r1^4*(-31-18*ur1^2+6*ur1^4)+M^2*r1^3*(827-1653*ur1^2+36*ur1^4)-2*M^3*r1^2*(301-450*ur1^2+180*ur1^4))))*ΔQ^6)/(3*r1^5*(a^2+r1*(-2*M+r1))^3)+(2*(4*a^9*e1*l1*M*(19*M+9*r1)-a^10*(73*M^2+42*M*r1+6*r1^2)+4*a^7*e1*l1*M*r1*(6*l1^2-88*M^2+r1^2*(59+36*ur1^2)+M*r1*(65+72*ur1^2))-4*a^5*e1*l1*M*r1^2*(-100*M^3+M*r1^2*(37-120*ur1^2)+8*M^2*r1*(41+18*ur1^2)-r1^3*(133+132*ur1^2)+6*l1^2*(5*M-r1*(5+ur1^2)))+12*a*e1*l1*M*r1^5*(l1^2*(36*M^2-6*M*r1*(5+2*ur1^2)+r1^2*(-25+6*ur1^2))+2*(2*M-r1)*r1^2*(11*M-r1*(7+10*ur1^2)))+4*a^3*e1*l1*M*r1^3*(3*l1^2*(12*M^2-2*M*r1*(21+2*ur1^2)+r1^2*(7+8*ur1^2))+r1*(300*M^3-4*M^2*r1*(37+60*ur1^2)-M*r1^2*(233+72*ur1^2)+r1^3*(125+156*ur1^2)))+a^8*(-(l1^2*(76*M^2+72*M*r1-3*(-5+e1^2)*r1^2))+r1*(358*M^3+6*r1^3*(-1+ur1^2)+24*M*r1^2*(-5+6*ur1^2)+M^2*r1*(-131+218*ur1^2)))-3*r1^5*(2*l1^4*(2*M-r1)*(20*M^2+r1^2*(-11+14*ur1^2)-M*r1*(19+16*ur1^2))+(2*M-r1)*r1^4*(48*M^2+2*M*r1*(-25+9*ur1^2)+r1^2*(13-8*ur1^2+3*ur1^4))+2*l1^2*r1^2*(84*M^3-2*M^2*r1*(63+9*e1^2+19*ur1^2)+r1^3*(5-23*e1^2+17*ur1^2-12*ur1^4)+8*M*r1^2*(4+3*e1^2+2*ur1^2+3*ur1^4)))-a^6*r1*(3*l1^4*(8*M+3*r1)+l1^2*(-352*M^3+3*r1^3*(4-10*e1^2+3*ur1^2)-6*M*r1^2*(-29+7*ur1^2)+8*M^2*(r1+36*r1*ur1^2))+r1*(556*M^4-3*r1^4*(19+2*ur1^2)+28*M^3*r1*(-31+34*ur1^2)+M^2*r1^2*(223+304*ur1^2-39*ur1^4)-6*M*r1^3*(-35+67*ur1^2+3*ur1^4)))+a^4*r1^2*(3*l1^4*(40*M^2-4*M*r1*(5+2*ur1^2)-r1^2*(1+4*ur1^2))+l1^2*(-400*M^4+9*r1^4*(7+13*e1^2+ur1^2)+16*M^3*r1*(43+36*ur1^2)-2*M^2*r1^2*(-64+573*ur1^2)-36*M*r1^3*(11-2*ur1^2+2*ur1^4))+3*r1*(88*M^5+4*M^4*r1*(-73+86*ur1^2)+M^2*r1^3*(-51-446*ur1^2+ur1^4)+r1^5*(49-10*ur1^2+2*ur1^4)+2*M*r1^4*(-76+71*ur1^2+7*ur1^4)-2*M^3*r1^2*(-225+8*ur1^2+13*ur1^4)))+3*a^2*r1^3*(-4*l1^4*(12*M^3+4*M*r1^2*(3+2*ur1^2)-2*M^2*r1*(13+2*ur1^2)-r1^3*(1+6*ur1^2))+r1^3*(-304*M^4+8*M^3*r1*(30+47*ur1^2)+2*M*r1^3*(-92+45*ur1^2+2*ur1^4)-4*M^2*r1^2*(-38+73*ur1^2+4*ur1^4)+r1^4*(43-18*ur1^2+5*ur1^4))+2*l1^2*r1*(-112*M^4+2*M^3*r1*(38+129*ur1^2)-3*M*r1^3*(35+8*ur1^2+4*ur1^4)+r1^4*(5+38*e1^2-2*ur1^2+12*ur1^4)+M^2*r1^2*(118-133*ur1^2+24*ur1^4))))*ΔQ^4*Δθ^2)/(3*r1^2*(a^2+r1*(-2*M+r1))^3)-(r1*(-108*a^7*e1*l1*M+3*a^8*(24*M+(2+e1^2)*r1)+12*a^5*e1*l1*M*r1*(37*M-8*r1*(5+ur1^2))+24*a^3*e1*l1*M*r1^2*(4*l1^2-19*M^2+4*M*r1*(15+2*ur1^2)-3*r1^2*(11+4*ur1^2))+a^6*(6*l1^2*(18*M+(3-2*e1^2)*r1)+r1*(-354*M^2+2*M*r1*(103+12*ur1^2)+r1^2*(-38+30*e1^2+15*ur1^2)))-12*a*e1*l1*M*r1^3*(4*l1^2*(2*M-r1*(5+3*ur1^2))+r1*(82*M^2+r1^2*(59+16*ur1^2)-M*r1*(97+32*ur1^2)))+r1^3*(24*l1^4*(2*M-r1)*(2*M-3*r1*(1+ur1^2))+r1^3*(504*M^3+4*(-212+27*e1^2)*M^2*r1+r1^3*(-179+138*e1^2-116*ur1^2-9*ur1^4)+2*M*r1^2*(328-72*e1^2+23*ur1^2+9*ur1^4))+l1^2*r1*(624*M^3-16*M^2*r1*(59+3*e1^2+3*ur1^2)+r1^3*(-125+69*ur1^2+36*ur1^4-72*e1^2*(1+ur1^2))+2*M*r1^2*(283-9*ur1^2+36*e1^2*(1+ur1^2))))+a^4*r1*(12*l1^4+r1*(552*M^3-2*M^2*r1*(370+9*ur1^2)+r1^3*(-201+117*e1^2+37*ur1^2-3*ur1^4)+2*M*r1^2*(270+7*ur1^2+12*ur1^4))+l1^2*(-444*M^2+24*M*r1*(13+4*ur1^2)-r1^2*(8-123*ur1^2+12*e1^2*(5+3*ur1^2))))-a^2*r1^2*(12*l1^4*(8*M-r1*(4+3*ur1^2))+2*r1*(132*M^4+2*M^3*r1*(-152+15*ur1^2)-3*M*r1^3*(153-5*ur1^2+5*ur1^4)+r1^4*(168-114*e1^2+11*ur1^2+6*ur1^4)+M^2*r1^2*(551+5*ur1^2+24*ur1^4))+l1^2*(-456*M^3+48*M^2*r1*(21+4*ur1^2)+14*M*r1^2*(-46+9*ur1^2)+r1^3*(79-156*ur1^2+12*e1^2*(10+9*ur1^2)))))*ΔQ^2*Δθ^4)/(6*(a^2+r1*(-2*M+r1))^3)+(r1^3*(48*a^5*e1*l1*M-3*a^6*(8*e1^2*M+r1)+48*a*e1*l1*M*r1^3*(-2*M+r1+r1*ur1^2)+48*a^3*e1*l1*M*r1*(-2*M+r1*(2+ur1^2))+r1^5*(4*M^2*(11+12*e1^2-33*ur1^2)+r1^2*(11-10*ur1^2+3*ur1^4)-2*M*r1*(22-43*ur1^2-9*ur1^4+12*e1^2*(1+ur1^2)))+a^4*(-24*l1^2*M+r1*(r1*(12*M+r1*(5-24*ur1^2))+24*e1^2*M*(2*M-r1*(3+ur1^2))))+a^2*r1*(24*l1^2*M*(2*M-r1*(1+ur1^2))+r1^2*(12*(-1+8*e1^2)*M^2+r1^2*(19-34*ur1^2+3*ur1^4)-2*M*r1*(16-57*ur1^2+12*e1^2*(3+2*ur1^2)))))*Δθ^6)/(24*(a^2+r1*(-2*M+r1))^3))+Δr*((16*ur1*(4*a^9*e1*M*(2*M+r1)^2*(4*M+3*r1)-a^8*l1*M*(64*M^3+102*M^2*r1+47*M*r1^2+6*r1^3)+6*a*e1*M*r1^7*(l1^4+7*l1^2*r1^2+6*r1^4)+2*a^7*e1*M*r1*(2*M+r1)*(3*l1^2*(7*M+4*r1)+4*r1^2*(12*M+7*r1))+2*a^3*e1*M*r1^4*(l1^4*(15*M+11*r1)+4*r1^4*(18*M+13*r1)+3*l1^2*r1^2*(19*M+16*r1))+2*a^5*e1*M*r1^2*(l1^4*(13*M+6*r1)+8*r1^3*(9*M^2+18*M*r1+7*r1^2)+3*l1^2*r1*(10*M^2+30*M*r1+13*r1^2))+3*l1*r1^7*(-6*l1^4*M+r1^4*(-8*M+r1+r1*ur1^2)+l1^2*r1^2*(-14*M+r1+4*r1*ur1^2))-a^6*l1*M*r1*(l1^2*(84*M^2+73*M*r1+12*r1^2)+r1*(60*M^3+2*M^2*r1*(164-51*ur1^2)+3*M*r1^2*(80-33*ur1^2)+6*r1^3*(7-4*ur1^2)))-a^4*l1*r1^2*(2*l1^4*M*(13*M+3*r1)+r1^3*(282*M^3-3*r1^3+M^2*r1*(355-87*ur1^2)+6*M*r1^2*(13-7*ur1^2))+3*l1^2*M*r1*(38*M^2+M*r1*(83-20*ur1^2)+2*r1^2*(11-4*ur1^2)))-3*a^2*l1*r1^4*(2*l1^4*M*(7*M+4*r1)+l1^2*r1^2*(68*M^2+30*M*r1-r1^2)-r1^4*(-58*M^2+r1^2*(2+ur1^2)+2*M*r1*(-11+4*ur1^2))))*ΔQ^6*ΔR)/(3*r1^6*(a^2+r1*(-2*M+r1)))+(4*ur1*(4*a^7*e1*M*(28*M^2+32*M*r1+9*r1^2)-a^6*l1*M*(112*M^2+99*M*r1+18*r1^2)+6*a*e1*M*r1^4*(9*l1^4+22*l1^2*r1^2+18*r1^4)+2*a^3*e1*M*r1^2*(9*l1^4+3*l1^2*r1*(35*M+29*r1)+2*r1^3*(72*M+55*r1))+2*a^5*e1*M*r1*(3*l1^2*(17*M+9*r1)+2*r1*(36*M^2+88*M*r1+37*r1^2))-a^4*l1*r1*(6*l1^2*M*(17*M+6*r1)+r1*(186*M^3-12*r1^3+M^2*r1*(323-39*ur1^2)+6*M*r1^2*(10-3*ur1^2)))+3*l1*r1^4*(l1^4*(-14*M+8*r1)+4*l1^2*r1^2*(-9*M+2*r1*(2+ur1^2))+3*r1^4*(-8*M+r1*(3+ur1^2)))-3*a^2*l1*r1^2*(6*l1^4*M+4*l1^2*r1*(17*M^2-3*r1^2+2*M*r1*(3+ur1^2))+r1^3*(100*M^2+4*M*r1*(7-2*ur1^2)-r1^2*(13+2*ur1^2))))*ΔQ^4*ΔR*Δθ^2)/(3*r1^3*(a^2+r1*(-2*M+r1)))+(ur1*(4*a^7*e1*M*(16*M+9*r1)-a^6*l1*(64*M^2+78*M*r1+15*r1^2)+2*a^5*e1*M*r1*(39*l1^2-64*M^2+68*M*r1+82*r1^2)-6*a*e1*M*r1^3*(8*l1^4+23*l1^2*(2*M-r1)*r1+18*(2*M-r1)*r1^3)-4*a^3*e1*M*r1^2*(l1^2*(39*M-54*r1)+r1*(72*M^2+28*M*r1-59*r1^2))+a^4*l1*r1*(128*M^3+14*M^2*r1-3*l1^2*(26*M+(9-4*e1^2)*r1)+r1^3*(-7+3*ur1^2)-2*M*r1^2*(61+12*ur1^2))+l1*r1^3*(24*l1^4*(2*M-r1)+l1^2*r1*(132*M^2-8*(11+3*e1^2)*M*r1+r1^2*(11+24*e1^2-12*ur1^2))+(2*M-r1)*r1^3*(72*M-r1*(35+9*ur1^2)))+a^2*l1*r1^2*(-12*l1^4+2*l1^2*(78*M^2-45*M*r1+2*(-4+9*e1^2)*r1^2)+r1*(156*M^3-6*M*r1^2*(27+5*ur1^2)+r1^3*(43+12*ur1^2)+2*M^2*r1*(35+24*ur1^2))))*ΔQ^2*ΔR*Δθ^4)/(3*(a^2+r1*(-2*M+r1))^2)+(r1^3*ur1*(12*a^5*e1*M-3*a^4*l1*((4+8*e1^2)*M+5*r1)+12*a*e1*M*r1^2*(4*l1^2+3*r1*(-2*M+r1))+24*a^3*e1*M*(2*l1^2+r1*(-M+2*r1))+l1*r1^4*(-2*M*(11+12*e1^2-9*ur1^2)+r1*(11+3*ur1^2))+a^2*l1*(-24*l1^2*M+r1*(24*M^2-6*(-3+8*e1^2)*M*r1+r1^2*(-4+3*ur1^2))))*ΔR*Δθ^6)/(12*(a^2+r1*(-2*M+r1))^2)))/(4*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*ΔQ^2+(r1^2*(a^2+r1*(-2*M+r1+r1*ur1^2))*Δr^2)/(a^2+r1*(-2*M+r1))^2+(2*l1*r1^2*ur1*Δr*ΔR)/(a^2-2*M*r1+r1^2)+r1^2*Δθ^2)^(7/2)+(-(r1^2*(a^2+r1*(-2*M+r1+r1*ur1^2))^2*(-6*a^7*e1*l1*M+a^8*(3*e1^2*M+r1)+2*a^5*e1*l1*M*r1*(14*M+5*r1*(-2+3*ur1^2))-4*a*e1*l1*M*r1^4*(6*M^2+M*r1*(-7+12*ur1^2)-2*r1^2*(-1+3*ur1^2+2*ur1^4))+2*a^3*e1*l1*M*r1^2*(-16*M^2+M*r1*(28-30*ur1^2)+r1^2*(-11+27*ur1^2+10*ur1^4))+M*r1^5*(12*M^3+2*M^2*r1*(-11+4*e1^2+3*ur1^2)+2*M*r1^2*(7-2*ur1^2-5*ur1^4+e1^2*(-5+9*ur1^2))+r1^3*(-3+5*ur1^4+2*ur1^6+e1^2*(3-9*ur1^2-6*ur1^4)))+a^6*(3*l1^2*M+r1*(e1^2*M*(-14*M+3*r1*(4-5*ur1^2))+r1*(-8*M+r1*(4+ur1^2))))+a^4*r1*(l1^2*M*(-14*M+r1*(8-15*ur1^2))+r1*(r1*(24*M^2+r1^2*(7+3*ur1^2)-M*r1*(25+3*ur1^2))+e1^2*M*(16*M^2+2*M*r1*(-19+15*ur1^2)+r1^2*(18-39*ur1^2-10*ur1^4))))+a^2*r1^2*(l1^2*M*(16*M^2+6*M*r1*(-3+5*ur1^2)-5*r1^2*(-1+3*ur1^2+2*ur1^4))+r1^2*(6*(-5+4*e1^2)*M^3+4*r1^3*(1+ur1^2)+2*M^2*r1*(23+e1^2*(-17+24*ur1^2))-M*r1^2*(24+7*ur1^2-5*ur1^4+e1^2*(-12+33*ur1^2+16*ur1^4)))))*Δr^9)/(8*(a^2+r1*(-2*M+r1))^9)-(16*ur1*(-4*a^11*e1*M^2*(2*M+r1)^2*(11*M+6*r1)+a^10*l1*M^2*(176*M^3+254*M^2*r1+119*M*r1^2+18*r1^3)+12*a*e1*M*r1^6*(2*l1^8+7*l1^6*r1^2+7*l1^4*r1^4+4*l1^2*r1^6+2*r1^8)+4*a^3*e1*M*r1^5*(21*l1^6*(2*M+r1)+r1^6*(12*M+19*r1)+2*l1^4*r1^2*(51*M+26*r1)+l1^2*r1^4*(54*M+41*r1))+4*a^5*e1*M*r1^4*(r1^4*(-45*M^2+14*M*r1+23*r1^2)+l1^4*(66*M^2+88*M*r1+27*r1^2)+l1^2*r1^2*(45*M^2+102*M*r1+44*r1^2))-4*a^7*e1*M*r1^2*(2*l1^4*M*(7*M+3*r1)+l1^2*r1*(30*M^3+12*M^2*r1-32*M*r1^2-15*r1^3)+r1^3*(132*M^3+129*M^2*r1+6*M*r1^2-13*r1^3))-4*a^9*e1*M*r1*(2*M+r1)*(l1^2*M*(25*M+12*r1)+r1*(42*M^3+71*M^2*r1+20*M*r1^2-3*r1^3))+3*l1*r1^6*(4*l1^8*M+18*l1^6*M*r1^2+3*l1^4*(12*M-r1)*r1^4+l1^2*r1^6*(28*M-3*r1-2*r1*ur1^2)+3*r1^8*(2*M+r1*ur1^2))+a^4*l1*M*r1^4*(l1^2*r1^2*(1734*M^2+M*r1*(1127-1014*ur1^2)+3*r1^2*(51-172*ur1^2))+r1^4*(1008*M^2+M*r1*(595-675*ur1^2)+9*r1^2*(6-41*ur1^2))+l1^4*(762*M^2+M*r1*(496-420*ur1^2)+6*r1^2*(12-35*ur1^2)))+3*a^2*l1*r1^5*(l1^2*r1^4*(206*M^2-3*r1^2+M*r1*(63-86*ur1^2))+2*l1^6*M*(26*M+r1*(9-10*ur1^2))+l1^4*M*r1^2*(172*M+7*r1*(9-10*ur1^2))+r1^6*(74*M^2+3*r1^2*ur1^2-9*M*r1*(-2+5*ur1^2)))+a^8*l1*M*r1*(l1^2*M*(200*M^2+175*M*r1+36*r1^2)+r1*(1020*M^4-90*r1^4*ur1^2+M^2*r1^2*(998-945*ur1^2)+18*M^3*r1*(100-33*ur1^2)-7*M*r1^3*(-25+72*ur1^2)))+a^6*l1*M*r1^2*(2*l1^4*M*(28*M+9*r1)+l1^2*r1*(1506*M^3+M*r1^2*(515-924*ur1^2)+30*r1^3*(1-8*ur1^2)-49*M^2*r1*(-35+18*ur1^2))+r1^3*(1782*M^3+5*M*r1^2*(106-225*ur1^2)+18*r1^3*(1-17*ur1^2)-3*M^2*r1*(-637+345*ur1^2))))*ΔQ^8*ΔR)/(3*r1^10)+(r1^2*ur1*(a^11*(-56*e1*M+6*e1*r1-6*e1^3*r1)+a^10*l1*(56*M+3*(3-5*e1^2)*r1)+2*a^9*e1*r1*(3*l1^2+200*M^2-2*M*r1*(84+13*ur1^2)-3*r1^2*(-11-2*ur1^2+e1^2*(11+ur1^2)))+2*a^7*e1*r1^2*(-526*M^3+4*M^2*r1*(223+25*ur1^2)+2*M*r1^2*(-249-77*ur1^2+26*ur1^4)+3*l1^2*(48*M+r1*(10+ur1^2))+3*r1^3*(52+19*ur1^2+ur1^4-e1^2*(52+9*ur1^2)))-2*a^5*e1*r1^3*(-600*M^4+2*M^3*r1*(851+42*ur1^2)+4*M^2*r1^2*(-431-108*ur1^2+62*ur1^4)-2*M*r1^3*(-501-223*ur1^2+62*ur1^4+35*ur1^6)+2*l1^2*(180*M^2-3*r1^2*(21+4*ur1^2)-34*M*r1*(13+10*ur1^2))+3*r1^4*(-140-75*ur1^2-8*ur1^4+e1^2*(140+33*ur1^2)))+a^8*l1*r1*(15*l1^2-400*M^2+2*M*r1*(99+26*ur1^2)+r1^2*(-8*e1^2*(19+15*ur1^2)+3*(38+41*ur1^2)))-2*a^3*e1*r1^4*(248*M^5+24*M^4*r1*(-52+ur1^2)+2*M^3*r1^2*(1049+148*ur1^2-145*ur1^4)+4*M^2*r1^3*(-494-195*ur1^2+104*ur1^4+37*ur1^6)-2*M*r1^4*(-746-395*ur1^2+26*ur1^4+63*ur1^6+10*ur1^8)+3*r1^5*(-238-163*ur1^2-25*ur1^4+e1^2*(238+65*ur1^2))-l1^2*(384*M^3+3*r1^3*(98+25*ur1^2)-8*M^2*r1*(183+151*ur1^2)+8*M*r1^2*(336+319*ur1^2+77*ur1^4)))-a^6*l1*r1^2*(-1052*M^3+8*M^2*r1*(163+25*ur1^2)+2*M*r1^2*(9+272*ur1^2+52*ur1^4)+l1^2*(288*M-r1*(137+120*ur1^2))+r1^3*(-668-866*ur1^2-289*ur1^4+e1^2*(774+793*ur1^2+175*ur1^4)))+a^4*l1*r1^3*(-1200*M^4+24*M^3*r1*(109+7*ur1^2)+8*M^2*r1^2*(-145+118*ur1^2+62*ur1^4)-2*M*r1^3*(939+1558*ur1^2+731*ur1^4+70*ur1^6)+l1^2*(720*M^2-2*M*r1*(817+680*ur1^2)+r1^2*(637+673*ur1^2+175*ur1^4))+r1^4*(2300+2801*ur1^2+1438*ur1^4+245*ur1^6-e1^2*(2422+2312*ur1^2+791*ur1^4+70*ur1^6)))+a^2*l1*r1^4*(496*M^5+16*M^4*r1*(-118+3*ur1^2)-4*M^3*r1^2*(-419+194*ur1^2+145*ur1^4)+4*M^2*r1^3*(447+950*ur1^2+523*ur1^4+74*ur1^6)-4*M*r1^4*(1538+1763*ur1^2+944*ur1^4+189*ur1^6+10*ur1^8)+l1^2*(-768*M^3+4*M^2*r1*(657+604*ur1^2)-2*M*r1^2*(2346+2243*ur1^2+616*ur1^4)+r1^3*(1785+1639*ur1^2+616*ur1^4+70*ur1^6))+r1^5*(4852+5554*ur1^2+3005*ur1^4+794*ur1^6+70*ur1^8-e1^2*(4900+3865*ur1^2+1414*ur1^4+178*ur1^6)))-4*a*e1*r1^5*(l1^2*(72*M^4-30*r1^4*(7+2*ur1^2)-4*M^3*r1*(125+88*ur1^2)+2*M^2*r1^2*(695+630*ur1^2+133*ur1^4)-M*r1^3*(2489+1980*ur1^2+665*ur1^4+54*ur1^6))+r1*(116*M^5+4*M^4*r1*(-95+18*e1^2-ur1^2)+30*r1^5*(-1+e1^2-ur1^2)*(7+2*ur1^2)+2*M^2*r1^3*(-341-177*ur1^2+35*ur1^4+30*ur1^6+15*e1^2*(7+2*ur1^2))+M^3*r1^2*(609+162*ur1^2-115*ur1^4-12*e1^2*(13+3*ur1^2))+M*r1^4*(649+407*ur1^2+38*ur1^4-28*ur1^6-8*ur1^8-3*e1^2*(75+22*ur1^2))))+l1*r1^5*(l1^2*(2*M-r1)*(144*M^3-4*M^2*r1*(199+176*ur1^2)+4*M*r1^2*(483+422*ur1^2+133*ur1^4)-r1^3*(3115+2226*ur1^2+798*ur1^4+108*ur1^6))+r1*(288*M^5+16*M^4*r1*(-25+14*e1^2+9*ur1^2)-r1^5*(-1+e1^2-ur1^2)*(3115+2226*ur1^2+798*ur1^4+108*ur1^6)-8*M^3*r1^2*(139+207*ur1^2+63*ur1^4+e1^2*(31-39*ur1^2))-4*M^2*r1^3*(-1102-1212*ur1^2-561*ur1^4-63*ur1^6+13*e1^2*(11+19*ur1^2+7*ur1^4))+2*M*r1^4*(-4062-4025*ur1^2-1961*ur1^4-437*ur1^6-18*ur1^8+e1^2*(945+876*ur1^2+357*ur1^4+38*ur1^6)))))*Δr^8*ΔR)/(16*(a^2+r1*(-2*M+r1))^8)+(4*ur1*(4*a^11*e1*M*(132*M^3+170*M^2*r1+70*M*r1^2+9*r1^3)-a^10*l1*M*(528*M^3+905*M^2*r1+535*M*r1^2+108*r1^3)-12*a*e1*M*r1^5*(10*l1^8+28*l1^6*(2*M-r1)*r1+32*l1^4*(2*M-r1)*r1^3+9*l1^2*(2*M-r1)*r1^5+8*r1^7*(-2*M+r1))-4*a^3*e1*M*r1^4*(21*l1^6*(10*M-9*r1)+l1^4*r1*(240*M^2+298*M*r1-305*r1^2)+l1^2*r1^3*(180*M^2+118*M*r1-131*r1^2)+3*r1^5*(-24*M^2-18*M*r1+23*r1^2))+4*a^9*e1*M*r1*(-264*M^4-76*M^3*r1+306*M^2*r1^2+192*M*r1^3+26*r1^4+l1^2*(269*M^2+260*M*r1+63*r1^2))+4*a^5*e1*M*r1^3*(105*l1^6+l1^4*(-500*M^2+112*M*r1+338*r1^2)+2*r1^3*(-90*M^3+3*M^2*r1+16*M*r1^2-29*r1^3)+l1^2*r1*(-198*M^3-577*M^2*r1+144*M*r1^2+246*r1^3))+4*a^7*e1*M*r1^2*(l1^4*(250*M+129*r1)+l1^2*(-538*M^3-152*M^2*r1+472*M*r1^2+205*r1^3)+2*r1*(-132*M^4-210*M^3*r1+43*M^2*r1^2+74*M*r1^3+2*r1^4))+a^8*l1*M*r1*(1056*M^4+76*M^3*r1-l1^2*(1076*M^2+1415*M*r1+456*r1^2)+54*r1^4*(-9+4*ur1^2)+9*M^2*r1^2*(-218+83*ur1^2)+M*r1^3*(-1796+801*ur1^2))+3*l1*r1^5*(20*l1^8*(2*M-r1)+l1^4*r1^3*(328*M^2-178*M*r1+7*r1^2)+2*(2*M-r1)*r1^7*(12*M+r1+6*r1*ur1^2)+2*l1^2*(2*M-r1)*r1^5*(63*M-r1*(4+3*ur1^2))+4*l1^6*r1*(34*M^2+5*r1^2*(-1+e1^2-ur1^2)+M*r1*(-7-5*e1^2+5*ur1^2)))-3*a^2*l1*r1^4*(10*l1^8-l1^4*r1*(360*M^3+620*M^2*r1-564*M*r1^2+7*r1^3)+l1^6*(-280*M^2+188*M*r1+10*r1^2*(3-3*e1^2+ur1^2))-l1^2*r1^3*(720*M^3+10*M^2*r1*(41-16*ur1^2)+r1^3*(13+6*ur1^2)+M*r1^2*(-521+80*ur1^2))+r1^5*(-276*M^3+3*r1^3*(2+7*ur1^2)-3*M*r1^2*(-42+37*ur1^2)+2*M^2*r1*(-41+93*ur1^2)))-a^4*l1*r1^3*(30*l1^6*(14*M+r1-e1^2*r1)-4*l1^4*M*(500*M^2-31*M*r1-477*r1^2)+3*r1^3*(-816*M^4+3*r1^4*(2+3*ur1^2)+10*M^2*r1^2*(25+3*ur1^2)-3*M*r1^3*(-94+89*ur1^2)+4*M^3*r1*(-130+159*ur1^2))-l1^2*r1*(2268*M^4+15*r1^4+M^2*r1^2*(-1087+18*ur1^2)+3*M*r1^3*(-803+172*ur1^2)-4*M^3*r1*(-974+285*ur1^2)))-a^6*l1*r1^2*(4*l1^4*M*(250*M+177*r1)-2*l1^2*M*(1076*M^3+310*M^2*r1+3*r1^3*(-285+46*ur1^2)+3*M*r1^2*(-503+95*ur1^2))+r1*(-2412*M^5+6*r1^5+M^2*r1^3*(2113-1323*ur1^2)+6*M*r1^4*(151-123*ur1^2)+6*M^4*r1*(-508+249*ur1^2)+M^3*r1^2*(397+855*ur1^2))))*ΔQ^6*ΔR*Δθ^2)/(3*r1^7*(a^2+r1*(-2*M+r1)))-(ur1*(-4*a^9*e1*M*(147*M^2+134*M*r1+30*r1^2)+a^8*l1*M*(588*M^2+959*M*r1+363*r1^2)+12*a*e1*M*r1^4*(35*l1^6+8*l1^4*(19*M-8*r1)*r1+51*l1^2*(2*M-r1)*r1^3+12*r1^5*(-2*M+r1))-4*a^7*e1*M*r1*(-294*M^3-76*M^2*r1+200*M*r1^2+73*r1^3+2*l1^2*(175*M+93*r1))+4*a^3*e1*M*r1^3*(l1^4*(504*M-471*r1)+2*l1^2*r1*(216*M^2+223*M*r1-242*r1^2)+3*r1^3*(-24*M^2-2*M*r1+19*r1^2))-4*a^5*e1*M*r1^2*(252*l1^4+l1^2*(-700*M^2+194*M*r1+517*r1^2)+r1*(-90*M^3-207*M^2*r1+4*M*r1^2+22*r1^3))+a^6*l1*r1*(-1176*M^4-1402*M^3*r1+5*r1^4+l1^2*(1400*M^2+1179*M*r1-9*(-1+e1^2)*r1^2)+M^2*r1^2*(1204-135*ur1^2)+M*r1^3*(1229-63*ur1^2))+a^2*l1*r1^3*(105*l1^6+r1^3*(180*M^3+3*M*r1^2*(233-27*ur1^2)+2*M^2*r1*(-692+27*ur1^2)+3*r1^3*(17+27*ur1^2))+l1^2*r1*(-324*M^3+r1^3*(65-108*e1^2+27*ur1^2)-16*M^2*r1*(211+30*ur1^2)+3*M*r1^2*(763+74*ur1^2))+l1^4*(-2016*M^2+1158*M*r1+r1^2*(338-315*e1^2+105*ur1^2)))+a^4*l1*r1^2*(3*l1^4*(336*M+(38-35*e1^2)*r1)+l1^2*(-2800*M^3-796*M^2*r1+r1^3*(37-54*e1^2+9*ur1^2)+10*M*r1^2*(293+24*ur1^2))+r1*(144*M^4+9*M*r1^3*(167-10*ur1^2)+3*r1^4*(11+9*ur1^2)-M^2*r1^2*(851+9*ur1^2)+2*M^3*r1*(-1007+135*ur1^2)))+l1*r1^4*(-210*l1^6*(2*M-r1)+l1^2*r1^3*(-1152*M^2+2*M*r1*(251+27*e1^2-9*ur1^2)+r1^2*(37-63*e1^2+45*ur1^2))-(2*M-r1)*r1^5*(108*M+r1*(23+54*ur1^2))+l1^4*r1*(-792*M^2+2*M*r1*(-53+105*e1^2-105*ur1^2)+r1^2*(251-210*e1^2+210*ur1^2))))*ΔQ^4*ΔR*Δθ^4)/(3*r1^4*(a^2+r1*(-2*M+r1)))-(ur1*(-4*a^7*e1*M*(70*M+33*r1)+4*a^5*e1*M*r1*(-177*l1^2+140*M^2+8*M*r1-50*r1^2)+a^6*l1*(280*M^2+429*M*r1-9*(-2+e1^2)*r1^2)+24*a*e1*M*r1^3*(23*l1^4+l1^2*(50*M-19*r1)*r1+4*r1^3*(-2*M+r1))+4*a^3*e1*M*r1^2*(6*l1^2*(59*M-53*r1)+r1*(-24*M^2+46*M*r1+7*r1^2))+a^4*l1*r1*(-560*M^3-1004*M^2*r1+6*l1^2*(118*M+(26-23*e1^2)*r1)+2*r1^3*(44-27*e1^2+9*ur1^2)+M*r1^2*(866+189*ur1^2))+l1*r1^3*(-276*l1^4*(2*M-r1)-2*l1^2*r1*(132*M^2+r1^2*(-164+138*e1^2-135*ur1^2)+2*M*r1*(131-69*e1^2+66*ur1^2))+r1^3*(-36*M^2+2*M*r1*(-82+27*e1^2-63*ur1^2)+r1^2*(91-63*e1^2+99*ur1^2)))+a^2*l1*r1^2*(138*l1^4+r1*(852*M^3+9*M*r1^2*(39+17*ur1^2)-14*M^2*r1*(98+27*ur1^2)+r1^3*(161-108*e1^2+90*ur1^2))+l1^2*(-1416*M^2+510*M*r1+r1^2*(457-414*e1^2+132*ur1^2))))*ΔQ^2*ΔR*Δθ^6)/(12*r1*(a^2+r1*(-2*M+r1)))-(r1^2*ur1*(-48*a^5*e1*M+3*a^4*l1*(2*(8+21*e1^2)*M+3*r1)-12*a*e1*M*r1^2*(21*l1^2+4*M*r1-2*r1^2)-12*a^3*e1*M*(21*l1^2+2*r1*(-4*M+r1))+l1*r1^3*(216*M^2+2*M*r1*(-65+63*e1^2-72*ur1^2)+r1^2*(11+9*ur1^2))+a^2*l1*(126*l1^2*M+r1*(-96*M^2+6*(-13+42*e1^2)*M*r1+r1^2*(20+9*ur1^2))))*ΔR*Δθ^8)/(48*(a^2+r1*(-2*M+r1)))+Δr^7*(((-4*a^13*e1*l1*(28*M+3*(-1+e1^2)*r1)+2*a^14*(28*M+(-5+8*e1^2)*r1)-4*a^11*e1*l1*r1*(-3*l1^2-234*M^2+M*r1*(293+114*ur1^2)+3*r1^2*(-13-4*ur1^2+e1^2*(13+3*ur1^2)))-4*a^9*e1*l1*r1^2*(750*M^3-2*M^2*r1*(883+377*ur1^2)+M*r1^2*(1584+523*ur1^2-54*ur1^4)-3*l1^2*(34*M+3*r1*(4+ur1^2))-9*r1^3*(25+15*ur1^2+ur1^4-e1^2*(25+11*ur1^2)))-4*a^7*e1*l1*r1^3*(-1124*M^4+4*M^3*r1*(1133+444*ur1^2)+2*M^2*r1^2*(-3186-1391*ur1^2+260*ur1^4)+M*r1^3*(5401+770*ur1^2-296*ur1^4-280*ur1^6)+3*l1^2*(112*M^2-3*r1^2*(21+10*ur1^2)-12*M*r1*(26+31*ur1^2))+9*r1^4*(-85-73*ur1^2-10*ur1^4+e1^2*(85+52*ur1^2)))-8*a^5*e1*l1*r1^4*(372*M^5-2*M^4*r1*(1405+426*ur1^2)+M^3*r1^2*(5904+2338*ur1^2-721*ur1^4)+M^2*r1^3*(-7084-1679*ur1^2+860*ur1^4+602*ur1^6)-M*r1^4*(-6141+59*ur1^2+468*ur1^4+385*ur1^6+70*ur1^8)+9*r1^5*(-95-102*ur1^2-21*ur1^4+e1^2*(95+70*ur1^2))-l1^2*(264*M^3+9*r1^3*(32+21*ur1^2)-4*M^2*r1*(274+369*ur1^2)+M*r1^2*(2138+3054*ur1^2+945*ur1^4)))-8*a^3*e1*l1*r1^5*(-72*M^6+8*M^5*r1*(205+32*ur1^2)+2*M^4*r1^2*(-2541-626*ur1^2+309*ur1^4)-4*M^3*r1^3*(-2192-427*ur1^2+382*ur1^4+161*ur1^6)-M*r1^5*(-9616+883*ur1^2+966*ur1^4+350*ur1^6+124*ur1^8)+M^2*r1^4*(-10316-285*ur1^2+1240*ur1^4+1064*ur1^6+140*ur1^8)+63*r1^6*(-21-26*ur1^2-7*ur1^4+e1^2*(21+17*ur1^2))+l1^2*(192*M^4-63*r1^4*(9+7*ur1^2)-8*M^3*r1*(158+213*ur1^2)+8*M^2*r1^2*(436+651*ur1^2+210*ur1^4)-2*M*r1^3*(2958+3867*ur1^2+1680*ur1^4+182*ur1^6)))+a^12*(2*l1^2*(56*M+r1-6*e1^2*r1)+r1*(-512*M^2+24*M*r1*(19+4*ur1^2)+r1^2*(-213+30*ur1^2+e1^2*(225-34*ur1^2))))+8*a*e1*l1*r1^6*(l1^2*(48*M^5+126*r1^5*(6+5*ur1^2)-48*M^4*r1*(14+15*ur1^2)+4*M^3*r1^2*(686+870*ur1^2+245*ur1^4)-4*M^2*r1^3*(1614+1953*ur1^2+805*ur1^4+77*ur1^6)+M*r1^4*(10495+11838*ur1^2+4655*ur1^4+770*ur1^6))+r1*(376*M^6+4*M^5*r1*(-415+36*e1^2-4*ur1^2)-126*r1^6*(-1+e1^2-ur1^2)*(6+5*ur1^2)-M^2*r1^4*(-9530+1173*ur1^2+1088*ur1^4+462*ur1^6+108*ur1^8+126*e1^2*(6+5*ur1^2))-2*M^4*r1^2*(-2233-118*ur1^2+331*ur1^4+12*e1^2*(16+9*ur1^2))+M^3*r1^3*(-7605+236*ur1^2+987*ur1^4+504*ur1^6+36*e1^2*(17+13*ur1^2))+M*r1^5*(-9993+1726*ur1^2+1173*ur1^4+105*ur1^6+54*ur1^8+e1^2*(798+675*ur1^2))))+a^10*r1*(12*l1^4+l1^2*(-936*M^2+2*M*r1*(409+228*ur1^2)-r1^2*(9-316*ur1^2+e1^2*(206+276*ur1^2)))+r1*(1832*M^3-2*M^2*r1*(1575+344*ur1^2)+2*M*r1^2*(1353+80*ur1^2+112*ur1^4)+r1^3*(-1477+224*ur1^2+90*ur1^4+e1^2*(1417-409*ur1^2-50*ur1^4))))+a^8*r1^2*(l1^4*(-408*M+2*r1*(97+138*ur1^2))+r1*(-3188*M^4+2*M^3*r1*(4489+894*ur1^2)-4*M^2*r1^2*(3100+345*ur1^2+388*ur1^4)+2*M*r1^3*(5381-466*ur1^2+92*ur1^4+212*ur1^6)+r1^4*(-5551+853*ur1^2+901*ur1^4+50*ur1^6+e1^2*(5311-2149*ur1^2-502*ur1^4)))+l1^2*(3000*M^3-2*M^2*r1*(2715+1508*ur1^2)-2*M*r1^2*(-1784+427*ur1^2+108*ur1^4)+r1^3*(318+2947*ur1^2+1014*ur1^4-2*e1^2*(818+1239*ur1^2+350*ur1^4))))-2*a^4*r1^4*(l1^4*(1056*M^3-16*M^2*r1*(257+369*ur1^2)+2*M*r1^2*(3892+5601*ur1^2+1890*ur1^4)-r1^3*(2996+4125*ur1^2+1890*ur1^4+210*ur1^6))+r1*(440*M^6-20*M^5*r1*(213+22*ur1^2)+2*M^4*r1^2*(7512+464*ur1^2+1117*ur1^4)-M^3*r1^3*(25502-1260*ur1^2+2653*ur1^4+1926*ur1^6)+2*M^2*r1^4*(13907-2244*ur1^2-1468*ur1^4+1048*ur1^6+236*ur1^8)+M*r1^5*(-23709+5698*ur1^2+6672*ur1^4+128*ur1^6-304*ur1^8-20*ur1^10)+r1^6*(11723-1720*ur1^2-4814*ur1^4-839*ur1^6+e1^2*(-11621+6430*ur1^2+2455*ur1^4)))+l1^2*(-1488*M^5+2*M^4*r1*(4549+1704*ur1^2)+M^3*r1^2*(-16395-1883*ur1^2+2884*ur1^4)-M^2*r1^3*(-13259+13018*ur1^2+9754*ur1^4+2408*ur1^6)+M*r1^4*(-2771+26274*ur1^2+15588*ur1^4+3696*ur1^6+280*ur1^8)+r1^5*(-6000-18539*ur1^2-10900*ur1^4-2828*ur1^6-210*ur1^8+14*e1^2*(762+963*ur1^2+435*ur1^4+67*ur1^6))))+2*a^2*r1^5*(l1^4*(2*M-r1)*(384*M^3-8*M^2*r1*(271+426*ur1^2)+6*M*r1^2*(856+1257*ur1^2+560*ur1^4)-r1^3*(7672+9357*ur1^2+4200*ur1^4+728*ur1^6))+r1*(16*M^7-16*M^6*r1*(75+4*ur1^2)+4*M^5*r1^2*(2013+68*ur1^2+237*ur1^4)-4*M^4*r1^3*(4769-266*ur1^2+422*ur1^4+267*ur1^6)+2*M^3*r1^4*(13908-2228*ur1^2-1293*ur1^4+943*ur1^6+192*ur1^8)+M*r1^6*(29646-8608*ur1^2-11035*ur1^4-1440*ur1^6+188*ur1^8+20*ur1^10)-M^2*r1^5*(30875-7588*ur1^2-8617*ur1^4+286*ur1^6+520*ur1^8+40*ur1^10)+r1^7*(-14773+1464*ur1^2+7522*ur1^4+1630*ur1^6+e1^2*(14749-8557*ur1^2-3493*ur1^4)))-l1^2*(288*M^6-4*M^5*r1*(1377+256*ur1^2)-8*M^4*r1^2*(-1829-43*ur1^2+309*ur1^4)+M^3*r1^3*(-17213+12522*ur1^2+10038*ur1^4+2576*ur1^6)-M^2*r1^4*(-8055+34925*ur1^2+22214*ur1^4+5992*ur1^6+560*ur1^8)+M*r1^5*(6768+52651*ur1^2+29378*ur1^4+7784*ur1^6+844*ur1^8)+r1^6*(-13377-34719*ur1^2-19971*ur1^4-5852*ur1^6-728*ur1^8+14*e1^2*(1461+1653*ur1^2+650*ur1^4+118*ur1^6))))+a^6*r1^3*(2*l1^4*(672*M^2-2*M*r1*(889+1116*ur1^2)+r1^2*(721+1101*ur1^2+350*ur1^4))+r1*(2680*M^5-8*M^4*r1*(1563+250*ur1^2)+16*M^3*r1^2*(1690+167*ur1^2+248*ur1^4)-2*M^2*r1^3*(16486-856*ur1^2+1275*ur1^4+1120*ur1^6)+2*M*r1^4*(13687-2344*ur1^2-1833*ur1^4+524*ur1^6+140*ur1^8)+r1^5*(-13577+2153*ur1^2+3882*ur1^4+464*ur1^6+e1^2*(13247-6544*ur1^2-2110*ur1^4)))-l1^2*(4496*M^4-2*M^3*r1*(7199+3552*ur1^2)+2*M^2*r1^2*(8329+635*ur1^2-1040*ur1^4)+2*M*r1^3*(-4016+7329*ur1^2+3706*ur1^4+560*ur1^6)+r1^4*(-3097-13206*ur1^2-7058*ur1^4-1120*ur1^6+2*e1^2*(3717+5226*ur1^2+2240*ur1^4+210*ur1^6))))-2*r1^6*(l1^4*(2*M-r1)*(96*M^4-16*M^3*r1*(77+90*ur1^2)+4*M^2*r1^2*(1058+1287*ur1^2+490*ur1^4)-8*M*r1^3*(1077+1230*ur1^2+525*ur1^4+77*ur1^6)+r1^4*(12782+13785*ur1^2+4900*ur1^4+924*ur1^6))+r1^3*(1448*M^6+4*M^5*r1*(-1315+204*e1^2+106*ur1^2)+r1^6*(-1+e1^2-ur1^2)*(-7700+4512*ur1^2+1867*ur1^4)+2*M^4*r1^2*(5467-936*ur1^2-659*ur1^4+28*e1^2*(-44+15*ur1^2))+M*r1^5*(-22754+5905*ur1^2+9643*ur1^4+1650*ur1^6-24*ur1^8+e1^2*(7358-4271*ur1^2-1738*ur1^4))+M^3*r1^3*(-16737+3958*ur1^2+4231*ur1^4+276*ur1^6-4*e1^2*(-1119+545*ur1^2+156*ur1^4))+2*M^2*r1^4*(10455-2761*ur1^2-3820*ur1^4-471*ur1^6+24*ur1^8+e1^2*(-3122+1729*ur1^2+646*ur1^4)))+l1^2*r1*(1416*M^6+4*M^5*r1*(-1251+152*e1^2+133*ur1^2)-2*M^4*r1^2*(-4163+2770*ur1^2+1078*ur1^4+120*e1^2*(5+ur1^2))+M^3*r1^3*(-7025+19761*ur1^2+9758*ur1^4+1344*ur1^6-40*e1^2*(5+24*ur1^2+28*ur1^4))+4*M^2*r1^4*(-139-10040*ur1^2-5189*ur1^4-1134*ur1^6-72*ur1^8+e1^2*(967+1212*ur1^2+770*ur1^4+98*ur1^6))+M*r1^5*(11426+59189*ur1^2+29368*ur1^4+7000*ur1^6+760*ur1^8-4*e1^2*(2142+2445*ur1^2+1120*ur1^4+203*ur1^6))+r1^6*(-5082-31079*ur1^2-20552*ur1^4-5824*ur1^6-924*ur1^8+e1^2*(12782+13785*ur1^2+4900*ur1^4+924*ur1^6)))))*ΔQ^2)/(8*(a^2+r1*(-2*M+r1))^8)+(r1^3*(a^12*(-7+4*e1^2)-104*a^9*e1*l1*M*r1+4*a^7*e1*l1*M*r1^2*(128*M+r1*(-239+118*ur1^2))-4*a^5*e1*l1*M*r1^3*(304*M^2+12*M*r1*(-67+25*ur1^2)+r1^2*(906-540*ur1^2-125*ur1^4))+4*a^3*e1*l1*M*r1^4*(352*M^3+8*M^2*r1*(-161+41*ur1^2)-4*M*r1^2*(-496+212*ur1^2+53*ur1^4)+r1^3*(-1924+1036*ur1^2+424*ur1^4-7*ur1^6))-4*a*e1*l1*M*r1^5*(160*M^4+8*M^3*r1*(-113+16*ur1^2)-4*M^2*r1^2*(-485+118*ur1^2+29*ur1^4)+2*M*r1^3*(-1273+434*ur1^2+184*ur1^4-7*ur1^6)+r1^4*(2575-1084*ur1^2-551*ur1^4+35*ur1^6+10*ur1^8))+a^10*(-4*l1^2+r1*(99*M+r1*(-84+30*ur1^2+e1^2*(61-34*ur1^2))))+a^6*r1^2*(l1^2*(-512*M^2+M*r1*(902-472*ur1^2)+r1^2*(-323+231*ur1^2+48*ur1^4))+r1*(1555*M^3+M^2*r1*(-3253+200*ur1^2)+M*r1^2*(2985-704*ur1^2-461*ur1^4)+r1^3*(-1452+503*ur1^2+544*ur1^4+54*ur1^6+e1^2*(1335-906*ur1^2-298*ur1^4))))+a^8*r1*(l1^2*(104*M+r1*(-57+34*ur1^2))+r1*(-551*M^2+M*r1*(821-170*ur1^2)+r1^2*(-455+190*ur1^2+91*ur1^4+e1^2*(380-265*ur1^2-48*ur1^4))))+a^4*r1^3*(l1^2*(2*M-r1)*(608*M^2+8*M*r1*(-146+75*ur1^2)+r1^2*(1012-675*ur1^2-250*ur1^4))+r1*(-2346*M^4+M^3*r1*(6335+454*ur1^2)+M^2*r1^2*(-7859+246*ur1^2+605*ur1^4)-M*r1^3*(-6391+1322*ur1^2+1789*ur1^4+120*ur1^6)+r1^4*(-3086+660*ur1^2+1445*ur1^4+246*ur1^6-10*ur1^8+2*e1^2*(1500-889*ur1^2-390*ur1^4+7*ur1^6+5*ur1^8))))+r1^5*(l1^2*(2*M-r1)*(320*M^4+16*M^3*r1*(-79+16*ur1^2)-4*M^2*r1^2*(-560+161*ur1^2+58*ur1^4)-4*M*r1^3*(664-236*ur1^2-121*ur1^4+7*ur1^6)+r1^4*(2590-1095*ur1^2-580*ur1^4+42*ur1^6+20*ur1^8))+r1*(-520*M^6+4*M^5*r1*(519-88*e1^2+174*ur1^2)+r1^6*(-1+e1^2-ur1^2)*(2590-1095*ur1^2-580*ur1^4+42*ur1^6+20*ur1^8)-2*M^4*r1^2*(2223+672*ur1^2+281*ur1^4+24*e1^2*(-23+ur1^2))+M^3*r1^3*(6637+1006*ur1^2+165*ur1^4+380*ur1^6+8*e1^2*(-239+36*ur1^2+10*ur1^4))+2*M^2*r1^4*(-3901-95*ur1^2+687*ur1^4-103*ur1^6-72*ur1^8+2*e1^2*(619-160*ur1^2-78*ur1^4+14*ur1^6))-2*M*r1^5*(-3932+205*ur1^2+1252*ur1^4+138*ur1^6-70*ur1^8-10*ur1^10+2*e1^2*(672-235*ur1^2-126*ur1^4+14*ur1^6+5*ur1^8))))+a^2*r1^4*(l1^2*(-1408*M^4-16*M^3*r1*(-281+82*ur1^2)+4*M^2*r1^2*(-1638+737*ur1^2+212*ur1^4)+4*M*r1^3*(1576-838*ur1^2-371*ur1^4+7*ur1^6)+r1^4*(-1988+1103*ur1^2+530*ur1^4-14*ur1^6-10*ur1^8))+r1*(1780*M^5-8*M^4*r1*(740+147*ur1^2)+M^3*r1^2*(9609+1444*ur1^2+187*ur1^4)+M^2*r1^3*(-10483+68*ur1^2+1449*ur1^4-166*ur1^6)+2*M*r1^4*(4652-748*ur1^2-1491*ur1^4-146*ur1^6+46*ur1^8)+r1^5*(-4602+166*ur1^2+2197*ur1^4+478*ur1^6-44*ur1^8-10*ur1^10+2*e1^2*(2289-1099*ur1^2-555*ur1^4+28*ur1^6+15*ur1^8)))))*Δθ^2)/(16*(a^2+r1*(-2*M+r1))^8))+Δr^6*((ur1*(2*a^12*l1*(16*M^2+348*M*r1+3*(16-13*e1^2)*r1^2)-2*a^13*e1*(16*M^2+156*M*r1+9*(-1+e1^2)*r1^2)+2*a^11*e1*r1*(152*M^3-9*l1^2*(74*M+(-7+6*e1^2)*r1)+16*M*r1^2*(-77+18*ur1^2)+4*M^2*r1*(395+118*ur1^2)+3*r1^3*(48+ur1^2+2*e1^2*(-24+ur1^2)))+a^10*l1*r1*(-304*M^3+12*l1^2*(111*M+8*(5-4*e1^2)*r1)+12*M*r1^2*(281+92*ur1^2)-8*M^2*r1*(753+118*ur1^2)+3*r1^3*(7*(69+22*ur1^2)-e1^2*(401+122*ur1^2)))-2*a^9*e1*r1^2*(-54*l1^4+444*M^4+18*M^3*r1*(363+188*ur1^2)-4*M^2*r1^2*(2281-33*ur1^2+332*ur1^4)-2*M*r1^3*(-2451+727*ur1^2+432*ur1^4)-3*r1^4*(333+17*ur1^2-2*ur1^4+e1^2*(-333+28*ur1^2))-3*l1^2*(1420*M^2+r1^2*(243-198*e1^2+16*ur1^2)-2*M*r1*(449+174*ur1^2)))+4*a^7*e1*r1^3*(232*M^5+6*l1^4*(278*M+45*r1)+306*M^4*r1*(23+13*ur1^2)-M^3*r1^2*(13230+2763*ur1^2+2944*ur1^4)+2*M^2*r1^3*(6497-1467*ur1^2-86*ur1^4+210*ur1^6)+M*r1^4*(-6258+1229*ur1^2+1826*ur1^4+210*ur1^6)+3*r1^5*(660+62*ur1^2-13*ur1^4+e1^2*(-660+82*ur1^2))-3*l1^2*(1575*M^3+r1^3*(-612+468*e1^2-77*ur1^2)-2*M^2*r1*(1111+292*ur1^2)+M*r1^2*(169+324*ur1^2-350*ur1^4)))+4*a^5*e1*r1^4*(-56*M^6-4*M^5*r1*(1955+769*ur1^2)+2*M^4*r1^2*(8821+3087*ur1^2+1616*ur1^4)+2*M^2*r1^4*(10844-2427*ur1^2-2246*ur1^4+168*ur1^6)+M*r1^5*(-11821+577*ur1^2+3044*ur1^4+588*ur1^6)-M^3*r1^3*(26432-2865*ur1^2+2656*ur1^4+840*ur1^6)+3*r1^6*(1659+254*ur1^2-69*ur1^4+e1^2*(-1659+262*ur1^2))+6*l1^4*(-684*M^2+189*r1^2+2*M*r1*(803+455*ur1^2))+3*l1^2*(1332*M^4+3*r1^4*(592-420*e1^2+103*ur1^2)-M^3*r1*(3043+234*ur1^2)+2*M^2*r1^2*(655+294*ur1^2-868*ur1^4)+M*r1^3*(3479+1090*ur1^2+924*ur1^4+420*ur1^6)))+12*a*e1*r1^6*(-4*l1^4*(128*M^4-315*r1^4-4*M^3*r1*(188+105*ur1^2)+2*M^2*r1^2*(1084+665*ur1^2+119*ur1^4)-M*r1^3*(3922+1995*ur1^2+595*ur1^4))+l1^2*r1*(764*M^5-4*M^4*r1*(307+108*e1^2+381*ur1^2)+r1^5*(2889-1260*e1^2+953*ur1^2)+M^3*r1^2*(6263+936*e1^2+2442*ur1^2+1568*ur1^4)+2*M*r1^4*(11963+675*e1^2+2288*ur1^2+112*ur1^4+154*ur1^6)-4*M^2*r1^3*(3729+315*e1^2+988*ur1^2+308*ur1^4+154*ur1^6))+r1^3*(-1628*M^5-2*M^4*r1*(-2002+324*e1^2+225*ur1^2)+r1^5*(-1+e1^2-ur1^2)*(-1629+307*ur1^2)+2*M*r1^4*(-2522-379*ur1^2+235*ur1^4+28*ur1^6+e1^2*(879-171*ur1^2))+M^3*r1^2*(-5271+389*ur1^2+856*ur1^4-216*e1^2*(-6+ur1^2))+2*M^2*r1^3*(2705+167*ur1^2-450*ur1^4-56*ur1^6+27*e1^2*(-31+6*ur1^2))))+4*a^3*e1*r1^5*(6*l1^4*(712*M^3+441*r1^3-4*M^2*r1*(632+385*ur1^2)+14*M*r1^2*(323+220*ur1^2+42*ur1^4))-3*l1^2*(268*M^5+r1^5*(-3285+2142*e1^2-689*ur1^2)+4*M^4*r1*(-130+119*ur1^2)+M^3*r1^2*(277-1296*ur1^2-2072*ur1^4)-2*M*r1^4*(6227+2006*ur1^2+399*ur1^4+364*ur1^6)+2*M^2*r1^3*(2985+1086*ur1^2+1484*ur1^4+420*ur1^6))+r1*(3480*M^6-4*M^5*r1*(2266+747*ur1^2)+2*M^4*r1^2*(10905-193*ur1^2+984*ur1^4)+M^3*r1^3*(-28470+5099*ur1^2+2504*ur1^4-672*ur1^6)+6*M*r1^5*(-2889-143*ur1^2+429*ur1^4+91*ur1^6)-2*M^2*r1^4*(-11833+1096*ur1^2+3104*ur1^4+210*ur1^6)+3*r1^6*(2772+643*ur1^2-193*ur1^4+4*e1^2*(-693+125*ur1^2))))+a^8*l1*r1^2*(384*l1^4+888*M^4+12*M^3*r1*(1705+564*ur1^2)+12*M*r1^3*(-35+48*ur1^2+244*ur1^4)-2*M^2*r1^2*(12837+5324*ur1^2+1328*ur1^4)+3*r1^4*(2775+1665*ur1^2+122*ur1^4-e1^2*(2741+1178*ur1^2))-3*l1^2*(2840*M^2-2*M*r1*(85+348*ur1^2)+r1^2*(-1629-946*ur1^2+2*e1^2*(607+350*ur1^2))))-2*a^6*l1*r1^3*(464*M^5+6*M^4*r1*(2909+1326*ur1^2)-M^3*r1^2*(33735+17492*ur1^2+5888*ur1^4)-3*M*r1^4*(-5079-3813*ur1^2+988*ur1^4+560*ur1^6)+M^2*r1^3*(10481+6469*ur1^2+11168*ur1^4+840*ur1^6)+3*l1^4*(1112*M-r1*(543+350*ur1^2))+3*r1^5*(-5379-3563*ur1^2-546*ur1^4+e1^2*(5536+2329*ur1^2))+3*l1^2*(-3150*M^3+M^2*r1*(1661+1168*ur1^2)+M*r1^2*(4599+2334*ur1^2+700*ur1^4)+r1^3*(-3920-3239*ur1^2-700*ur1^4+10*e1^2*(283+217*ur1^2+35*ur1^4))))+2*a^4*l1*r1^4*(112*M^6+8*M^5*r1*(1908+769*ur1^2)-2*M^4*r1^2*(19668+10915*ur1^2+3232*ur1^4)+M^3*r1^3*(22915+14699*ur1^2+22894*ur1^4+1680*ur1^6)-3*M^2*r1^4*(-6963-7184*ur1^2+5000*ur1^4+2464*ur1^6)+3*M*r1^5*(-18649-12900*ur1^2-868*ur1^4+1176*ur1^6+140*ur1^8)+3*r1^6*(14494+9188*ur1^2+1855*ur1^4-e1^2*(14702+4897*ur1^2))+3*l1^4*(2736*M^2-2*M*r1*(2971+1820*ur1^2)+r1^2*(2287+1820*ur1^2+350*ur1^4))-3*l1^2*(2664*M^4-13*M^3*r1*(161+36*ur1^2)-2*M^2*r1^2*(4308+2723*ur1^2+1736*ur1^4)+4*M*r1^3*(5129+3575*ur1^2+1162*ur1^4+210*ur1^6)+r1^4*(-12333-9654*ur1^2-3346*ur1^4-350*ur1^6+14*e1^2*(585+405*ur1^2+109*ur1^4))))-6*a^2*l1*r1^5*(l1^4*(2*M-r1)*(1424*M^2-2*M*r1*(1941+1540*ur1^2)+r1^2*(5903+3850*ur1^2+1176*ur1^4))+r1*(1832*M^6-4*M^5*r1*(1479+607*ur1^2)+2*M^4*r1^2*(2111+1438*ur1^2+1946*ur1^4)+M^3*r1^3*(6165+7070*ur1^2-4850*ur1^4-2128*ur1^6)+M*r1^5*(39834+21203*ur1^2+3648*ur1^4-672*ur1^6-140*ur1^8)+M^2*r1^4*(-23981-17373*ur1^2-390*ur1^4+2296*ur1^6+280*ur1^8)+r1^6*(-26653-16104*ur1^2-3116*ur1^4+e1^2*(26717+5823*ur1^2)))+l1^2*(-536*M^5-8*M^4*r1*(94+119*ur1^2)+2*M^3*r1^2*(5052+3549*ur1^2+2072*ur1^4)-M^2*r1^3*(29831+20410*ur1^2+8064*ur1^4+1680*ur1^6)+M*r1^4*(49779+28014*ur1^2+9380*ur1^4+1876*ur1^6)+r1^5*(-25911-16929*ur1^2-6454*ur1^4-1176*ur1^6+14*e1^2*(1117+575*ur1^2+186*ur1^4))))+6*l1*r1^6*(l1^4*(2*M-r1)*(512*M^3-12*M^2*r1*(207+140*ur1^2)+4*M*r1^2*(1506+875*ur1^2+238*ur1^4)-3*r1^3*(3245+1400*ur1^2+476*ur1^4))+r1^3*(-940*M^5+2*M^4*r1*(1918-228*e1^2+1607*ur1^2)+M^3*r1^2*(-13839-8675*ur1^2-1148*ur1^4+4*e1^2*(409+408*ur1^2))+r1^5*(16376+19087*ur1^2+2711*ur1^4-3*e1^2*(5456+909*ur1^2))-2*M^2*r1^3*(-14762-7622*ur1^2-1293*ur1^4+56*ur1^6+e1^2*(3017+1558*ur1^2))+M*r1^4*(-44475-20323*ur1^2-3122*ur1^4+56*ur1^6+e1^2*(11695+3298*ur1^2)))+l1^2*r1*(-1116*M^5+4*M^4*r1*(1345+236*e1^2+637*ur1^2)+M^3*r1^2*(-19963-10290*ur1^2-1792*ur1^4+112*e1^2*(-9+5*ur1^2))+M*r1^4*(-70097-26412*ur1^2-7756*ur1^4-1288*ur1^6+28*e1^2*(210+130*ur1^2+43*ur1^4))+2*M^2*r1^3*(22231+9934*ur1^2+2688*ur1^4+336*ur1^6-4*e1^2*(209+280*ur1^2+63*ur1^4))+r1^5*(26127+16646*ur1^2+5628*ur1^4+1428*ur1^6-3*e1^2*(3245+1400*ur1^2+476*ur1^4)))))*ΔQ^2*ΔR)/(24*r1*(a^2+r1*(-2*M+r1))^7)+(r1^2*ur1*(a^11*(-98*e1*M+6*e1*r1-6*e1^3*r1)+a^10*l1*(98*M+(53-44*e1^2)*r1)+2*a^9*e1*r1*(3*l1^2+370*M^2+3*r1^2*(11-11*e1^2+ur1^2)+5*M*r1*(-59+15*ur1^2))+2*a^7*e1*r1^2*(-1037*M^3+l1^2*(316*M+30*r1)+2*M^2*r1*(853-240*ur1^2)+6*r1^3*(26-26*e1^2+5*ur1^2)+M*r1^2*(-771+232*ur1^2+194*ur1^4))+a^6*l1*r1^2*(2074*M^3+5*M^2*r1*(-401+192*ur1^2)-M*r1^2*(544+1527*ur1^2+388*ur1^4)+r1^3*(1183+1222*ur1^2+164*ur1^4-6*e1^2*(217+145*ur1^2))+l1^2*(-632*M+r1*(303+146*ur1^2)))+a^8*l1*r1*(44*l1^2-740*M^2-3*M*r1*(-39+50*ur1^2)+r1^2*(31*(11+7*ur1^2)-e1^2*(347+146*ur1^2)))+2*a^5*e1*r1^3*(1276*M^4+42*r1^4*(10-10*e1^2+3*ur1^2)+M^3*r1*(-3521+1027*ur1^2)-2*M^2*r1^2*(-1493+579*ur1^2+392*ur1^4)+M*r1^3*(-1259+185*ur1^2+544*ur1^4+70*ur1^6)+l1^2*(-696*M^2+126*r1^2+4*M*r1*(369+181*ur1^2)))-2*a^3*e1*r1^4*(580*M^5+42*r1^5*(-17+17*e1^2-7*ur1^2)+2*M^4*r1*(-1420+367*ur1^2)+M^3*r1^2*(3863-1632*ur1^2-792*ur1^4)-2*M*r1^4*(-795-72*ur1^2+245*ur1^4+63*ur1^6)+2*M^2*r1^3*(-1349+407*ur1^2+708*ur1^4+70*ur1^6)-2*l1^2*(296*M^3+147*r1^3-4*M^2*r1*(232+143*ur1^2)+2*M*r1^2*(823+572*ur1^2-21*ur1^4)))-2*a*e1*r1^5*(r1*(620*M^5+420*r1^5*(-1+e1^2-ur1^2)+2*M^4*r1*(-718+72*e1^2+261*ur1^2)-M^3*r1^2*(-1635+312*e1^2+605*ur1^2+640*ur1^4)-2*M*r1^4*(-653+225*e1^2-191*ur1^2+70*ur1^4+28*ur1^6)+4*M^2*r1^3*(-367+105*e1^2+2*ur1^2+150*ur1^4+28*ur1^6))+4*l1^2*(32*M^4-105*r1^4-4*M^3*r1*(34+35*ur1^2)+2*M^2*r1^2*(278+207*ur1^2-21*ur1^4)+M*r1^3*(-1198-665*ur1^2+105*ur1^4+35*ur1^6)))+a^4*l1*r1^3*(-2552*M^4+M^3*r1*(5197-2054*ur1^2)+M^2*r1^2*(-2150+3307*ur1^2+1568*ur1^4)-M*r1^3*(2645+4317*ur1^2+1132*ur1^4+140*ur1^6)+l1^2*(2*M-r1)*(696*M-r1*(999+724*ur1^2))+r1^4*(7*(418+445*ur1^2+98*ur1^4-10*ur1^6)+e1^2*(-3094-2154*ur1^2+84*ur1^4+70*ur1^6)))+a^2*l1*r1^4*(1160*M^5+4*M^4*r1*(-1192+367*ur1^2)+M^3*r1^2*(4872-1643*ur1^2-1584*ur1^4)+2*M*r1^4*(-3206-3135*ur1^2-482*ur1^4+182*ur1^6)+M^2*r1^3*(467+3671*ur1^2+1022*ur1^4+280*ur1^6)+l1^2*(-1184*M^3+4*M^2*r1*(841+572*ur1^2)+4*M*r1^2*(-1394-1001*ur1^2+42*ur1^4)+r1^3*(2095+1430*ur1^2-84*ur1^4-70*ur1^6))+r1^5*(5062+4873*ur1^2+1114*ur1^4-294*ur1^6-70*ur1^8+e1^2*(-5110-2830*ur1^2+336*ur1^4+210*ur1^6)))+l1*r1^5*(l1^2*(2*M-r1)*(128*M^3-28*M^2*r1*(19+20*ur1^2)-4*M*r1^2*(-406-277*ur1^2+42*ur1^4)+r1^3*(-3015-1400*ur1^2+252*ur1^4+140*ur1^6))+r1*(1220*M^5+2*M^4*r1*(-1138+312*e1^2-613*ur1^2)+M^3*r1^2*(697+697*ur1^2+1204*ur1^4-48*e1^2*(19+ur1^2))+2*M^2*r1^3*(1622+1145*ur1^2-505*ur1^4-364*ur1^6+4*e1^2*(5-64*ur1^2+42*ur1^4))-2*M*r1^4*(3825+2686*ur1^2+52*ur1^4-406*ur1^6-70*ur1^8+2*e1^2*(-380-274*ur1^2+84*ur1^4+35*ur1^6))+r1^5*(3031+4423*ur1^2+1140*ur1^4-392*ur1^6-140*ur1^8+e1^2*(-3015-1400*ur1^2+252*ur1^4+140*ur1^6)))))*ΔR*Δθ^2)/(16*(a^2+r1*(-2*M+r1))^7))+Δr^5*(((-2*a^13*e1*l1*(100*M^2+22*M*r1+9*(-1+e1^2)*r1^2)+a^14*(136*M^2+4*M*r1+11*(-1+e1^2)*r1^2)-2*a^11*e1*l1*r1*(-440*M^3+3*l1^2*(46*M-9*r1+6*e1^2*r1)+14*M*r1^2*(32+13*ur1^2)+4*M^2*r1*(110+147*ur1^2)+9*r1^3*(-16+ur1^2-2*e1^2*(-8+ur1^2)))+2*a^9*e1*l1*r1^2*(18*l1^4-84*M^4+6*M^3*r1*(269+188*ur1^2)+4*M^2*r1^2*(55-654*ur1^2+820*ur1^4)+2*M*r1^3*(-1994+201*ur1^2+1024*ur1^4)+9*r1^4*(111-13*ur1^2-2*ur1^4+e1^2*(-111+28*ur1^2))+3*l1^2*(216*M^2+3*(37-22*e1^2)*r1^2-4*M*r1*(59+163*ur1^2)))-4*a^7*e1*l1*r1^3*(872*M^5-6*l1^4*(46*M+15*r1)-2*M^4*r1*(197+627*ur1^2)+M^3*r1^2*(-1222-3387*ur1^2+7856*ur1^4)+2*M^2*r1^3*(-3253+2544*ur1^2+276*ur1^4-1050*ur1^6)-M*r1^4*(-8362+4217*ur1^2+4172*ur1^4+1050*ur1^6)+9*r1^5*(-220+34*ur1^2+13*ur1^4+e1^2*(220-82*ur1^2))+3*l1^2*(83*M^3+3*r1^3*(-100+52*e1^2+3*ur1^2)-8*M^2*r1*(35+169*ur1^2)+M*r1^2*(119+1048*ur1^2)))-4*a^5*e1*l1*r1^4*(-952*M^6+4*M^5*r1*(757+603*ur1^2)-2*M^4*r1^2*(-421+121*ur1^2+4576*ur1^4)-4*M^2*r1^4*(5591-4548*ur1^2-2690*ur1^4+399*ur1^6)-M*r1^5*(-21337+16385*ur1^2+6522*ur1^4+2898*ur1^6)+M^3*r1^3*(10524-11243*ur1^2+7120*ur1^4+4200*ur1^6)+9*r1^6*(-553+90*ur1^2+69*ur1^4+e1^2*(553-262*ur1^2))+18*l1^4*(32*M^2-21*r1^2-14*M*r1*(7+10*ur1^2))+3*l1^2*(228*M^4+3*r1^4*(-312+140*e1^2+27*ur1^2)+M^3*r1*(-389+1494*ur1^2)+4*M^2*r1^2*(-14-741*ur1^2+175*ur1^4)+M*r1^3*(-1621+1066*ur1^2+70*ur1^4-700*ur1^6)))-4*a^3*e1*l1*r1^5*(-6*l1^4*(72*M^3+147*r1^3-18*M^2*r1*(22+35*ur1^2)+4*M*r1^2*(243+315*ur1^2+140*ur1^4))-3*l1^2*(292*M^5+4*M^4*r1*(-352+47*ur1^2)-3*r1^5*(-619+238*e1^2+95*ur1^2)+M^3*r1^2*(959-928*ur1^2+1400*ur1^4)-4*M^2*r1^3*(859-441*ur1^2+280*ur1^4+350*ur1^6)+2*M*r1^4*(3915-648*ur1^2-70*ur1^4+588*ur1^6))+r1*(-1896*M^6+4*M^5*r1*(166+537*ur1^2)-2*M^4*r1^2*(5087-2775*ur1^2+2832*ur1^4)+10*M^2*r1^4*(-3761+3363*ur1^2+1378*ur1^4+210*ur1^6)-2*M*r1^5*(-18115+17016*ur1^2+2374*ur1^4+1323*ur1^6)+M^3*r1^3*(27458-26177*ur1^2-5824*ur1^4+3192*ur1^6)+9*r1^6*(-924+119*ur1^2+193*ur1^4+e1^2*(924-500*ur1^2))))-a^12*(-(l1^2*(200*M^2+146*M*r1+(-35+24*e1^2)*r1^2))+r1*(728*M^3-2*M*r1^2*(349+24*ur1^2)-4*M^2*r1*(431+168*ur1^2)+r1^3*(97-54*ur1^2+e1^2*(-187+65*ur1^2))))-4*a*e1*l1*r1^6*(6*l1^4*(8*M^4-210*r1^4-4*M^3*r1*(43+70*ur1^2)+2*M^2*r1^2*(433+385*ur1^2+210*ur1^4)-M*r1^3*(1949+1330*ur1^2+1050*ur1^4))-3*l1^2*r1*(780*M^5-3*r1^5*(-683+140*e1^2+167*ur1^2)-4*M^4*r1*(261+36*e1^2+307*ur1^2)+M^3*r1^2*(3907+312*e1^2+582*ur1^2+1120*ur1^4)+2*M*r1^4*(8798+225*e1^2-2144*ur1^2-35*ur1^4+238*ur1^6)-2*M^2*r1^3*(4925+210*e1^2-840*ur1^2+210*ur1^4+476*ur1^6))+r1^3*(4236*M^5-9*r1^5*(-1+e1^2-ur1^2)*(-543+307*ur1^2)+6*M^4*r1*(-2210+324*e1^2+1847*ur1^2)+3*M^3*r1^2*(8709-7503*ur1^2-1856*ur1^4+648*e1^2*(-2+ur1^2))+2*M^2*r1^3*(-17801+17262*ur1^2+2622*ur1^4+798*ur1^6-81*e1^2*(-31+18*ur1^2))+2*M*r1^4*(18874-20137*ur1^2-849*ur1^4-399*ur1^6+9*e1^2*(-293+171*ur1^2))))+a^10*r1*(6*l1^4*(46*M+(5-9*e1^2)*r1)+l1^2*(-880*M^3+4*M^2*r1*(55+294*ur1^2)+2*M*r1^2*(926+1079*ur1^2)+r1^3*(34+239*ur1^2-6*e1^2*(-4+33*ur1^2)))+r1*(228*M^4-6*M^3*r1*(1797+620*ur1^2)+24*M^2*r1^2*(37+194*ur1^2+73*ur1^4)+2*M*r1^3*(1547-240*ur1^2+480*ur1^4)+r1^4*(-1163+835*ur1^2+51*ur1^4+e1^2*(1397-975*ur1^2+14*ur1^4))))+a^8*r1^2*(54*l1^6-6*l1^4*(216*M^2-2*M*r1*(49+326*ur1^2)+r1^2*(-121-217*ur1^2+e1^2*(97+175*ur1^2)))+l1^2*(168*M^4-6*M^3*r1*(483+376*ur1^2)+2*M*r1^3*(2562+2397*ur1^2+1312*ur1^4)-4*M^2*r1^2*(1611+1928*ur1^2+1640*ur1^4)+r1^4*(831+2806*ur1^2+184*ur1^4-6*e1^2*(296+261*ur1^2)))+r1*(4888*M^5+16*M^4*r1*(1450+429*ur1^2)-16*M^3*r1^2*(1010+1437*ur1^2+609*ur1^4)+2*M*r1^4*(5704-3738*ur1^2+1701*ur1^4+668*ur1^6)+2*M^2*r1^3*(-4139+7578*ur1^2+306*ur1^4+1028*ur1^6)+r1^5*(-6025+5175*ur1^2+674*ur1^4-14*ur1^6+e1^2*(6061-6240*ur1^2+182*ur1^4))))+2*a^6*r1^3*(l1^6*(-552*M+3*r1*(88+175*ur1^2))+l1^2*(1744*M^5+M^4*r1*(2050-2508*ur1^2)+M^3*r1^2*(3373+8059*ur1^2+15712*ur1^4)+4*M*r1^4*(1163-2012*ur1^2+502*ur1^4+525*ur1^6)-M^2*r1^3*(9067+7100*ur1^2+15208*ur1^4+4200*ur1^6)+r1^5*(4132+6088*ur1^2+654*ur1^4-3*e1^2*(2264+657*ur1^2)))+3*l1^4*(166*M^3+2*M*r1^2*(-452+227*ur1^2)-2*M^2*r1*(99+1352*ur1^2)+r1^3*(832+1353*ur1^2+525*ur1^4-e1^2*(544+1015*ur1^2+350*ur1^4)))+r1*(-4936*M^6-4*M^5*r1*(2447+582*ur1^2)+2*M^4*r1^2*(8564+9144*ur1^2+4695*ur1^4)-M^3*r1^3*(-1490+27378*ur1^2+5973*ur1^4+4240*ur1^6)+2*M^2*r1^4*(-8313+10047*ur1^2-1896*ur1^4-346*ur1^6+210*ur1^8)+M*r1^5*(16769-16890*ur1^2+960*ur1^4+2392*ur1^6+210*ur1^8)+r1^6*(-8701+8838*ur1^2+2197*ur1^4-84*ur1^6+e1^2*(8503-11180*ur1^2+483*ur1^4))))+2*r1^6*(6*l1^6*(2*M-r1)*(8*M^3-8*M^2*r1*(24+35*ur1^2)+7*M*r1^2*(98+75*ur1^2+60*ur1^4)-5*r1^3*(257+140*ur1^2+126*ur1^4))+l1^2*r1^3*(2712*M^5+12*M^4*r1*(-765+96*e1^2+1529*ur1^2)+6*M^3*r1^2*(385-7124*ur1^2-694*ur1^4+16*e1^2*(-17+36*ur1^2))+r1^5*(24143+45322*ur1^2-10320*ur1^4+171*e1^2*(-208+53*ur1^2))+M^2*r1^3*(24431+55959*ur1^2+4044*ur1^4+588*ur1^6-84*e1^2*(92+57*ur1^2))-M*r1^4*(60101+57239*ur1^2-4665*ur1^4+294*ur1^6+6*e1^2*(-3712+267*ur1^2)))-3*l1^4*r1*(664*M^5-4*M^4*r1*(452+108*e1^2+387*ur1^2)+2*M^3*r1^2*(4147+1911*ur1^2+700*ur1^4+4*e1^2*(83+35*ur1^2))+2*M^2*r1^3*(-10915-1134*ur1^2-1820*ur1^4-504*ur1^6+14*e1^2*(1+10*ur1^2+10*ur1^4))-2*M*r1^4*(-18963+891*ur1^2-2380*ur1^4-672*ur1^6+5*e1^2*(131+98*ur1^2+98*ur1^4))+r1^5*(-14450-901*ur1^2-2660*ur1^4-1260*ur1^6+10*e1^2*(257+140*ur1^2+126*ur1^4)))+r1^5*(4320*M^5+12*M^4*r1*(-1113+198*e1^2+937*ur1^2)+6*M^3*r1^2*(3916-4717*ur1^2-829*ur1^4+90*e1^2*(-11+13*ur1^2))+M*r1^4*(33925-44913*ur1^2-14412*ur1^4+1140*ur1^6+e1^2*(-11000+18135*ur1^2-1134*ur1^4))+M^2*r1^3*(-30907+40446*ur1^2+10455*ur1^4-864*ur1^6+36*e1^2*(253-390*ur1^2+21*ur1^4))+r1^5*(-11473+7524*ur1^2+17824*ur1^4-1173*ur1^6+e1^2*(11473-19045*ur1^2+1197*ur1^4))))+2*a^4*r1^4*(6*l1^6*(192*M^2-24*M*r1*(23+35*ur1^2)+r1^2*(228+420*ur1^2+175*ur1^4))+l1^2*(-1904*M^6+4*M^5*r1*(-199+1206*ur1^2)-4*M^4*r1^2*(160+2807*ur1^2+4576*ur1^4)+M^3*r1^3*(12295+6450*ur1^2+36898*ur1^4+8400*ur1^6)-M^2*r1^4*(15897-24849*ur1^2+14324*ur1^4+15876*ur1^6)+M*r1^5*(-3521-37411*ur1^2-1924*ur1^4+3906*ur1^6+1260*ur1^8)+r1^6*(18355+14707*ur1^2+1221*ur1^4+3*e1^2*(-8272+39*ur1^2)))+3*l1^4*(456*M^4+2*M^3*r1*(-413+1494*ur1^2)+2*M^2*r1^2*(1125-943*ur1^2+700*ur1^4)-2*M*r1^3*(3152+1916*ur1^2+1225*ur1^4+700*ur1^6)+r1^4*(3752+3322*ur1^2+2310*ur1^4+350*ur1^6-21*e1^2*(88+115*ur1^2+70*ur1^4)))+r1*(2832*M^7+144*M^6*r1*(17+3*ur1^2)-12*M^5*r1^2*(993+814*ur1^2+525*ur1^4)+4*M^4*r1^3*(551+7935*ur1^2+1824*ur1^4+1092*ur1^6)-3*M^2*r1^5*(11884-14482*ur1^2+885*ur1^4+1908*ur1^6)-6*M^3*r1^4*(-3758+6347*ur1^2-308*ur1^4+236*ur1^6+140*ur1^8)+2*M*r1^6*(16403-19956*ur1^2-3069*ur1^4+1567*ur1^6+210*ur1^8)+r1^7*(-16454+18628*ur1^2+7251*ur1^4-417*ur1^6+e1^2*(16247-24765*ur1^2+1351*ur1^4))))+2*a^2*r1^5*(-3*l1^6*(2*M-r1)*(144*M^2-36*M*r1*(19+35*ur1^2)+r1^2*(1392+1575*ur1^2+1120*ur1^4))+l1^2*r1*(888*M^6+12*M^5*r1*(-69+323*ur1^2)-6*M^4*r1^2*(1403+280*ur1^2+3046*ur1^4)+M^3*r1^3*(20039-36801*ur1^2+15714*ur1^4+14952*ur1^6)+M^2*r1^4*(-1369+67018*ur1^2+2658*ur1^4-11088*ur1^6-2520*ur1^8)+M*r1^5*(-38751-60135*ur1^2-3475*ur1^4+1512*ur1^6+1260*ur1^8)+r1^6*(44247+24473*ur1^2-2137*ur1^4+3*e1^2*(-18160+3489*ur1^2)))-3*l1^4*(584*M^5+376*M^4*r1*(-5+ur1^2)+2*M^3*r1^2*(1719+363*ur1^2+1400*ur1^4)+2*M*r1^4*(10536+2927*ur1^2+3045*ur1^4+1302*ur1^6)-2*M^2*r1^3*(5173+2593*ur1^2+2450*ur1^4+1400*ur1^6)+r1^5*(-10258-3851*ur1^2-3955*ur1^4-1120*ur1^6+7*e1^2*(566+425*ur1^2+340*ur1^4)))+r1^3*(1704*M^6-12*M^5*r1*(-5+856*ur1^2)-6*M^4*r1^2*(2691-3576*ur1^2+215*ur1^4)+M^3*r1^3*(35561-43242*ur1^2+1695*ur1^4+3840*ur1^6)-2*M^2*r1^4*(22307-29157*ur1^2-4374*ur1^4+2244*ur1^6+210*ur1^8)+M*r1^5*(43466-57828*ur1^2-14403*ur1^4+2256*ur1^6+210*ur1^8)+r1^6*(-21700+25011*ur1^2+14122*ur1^4-946*ur1^6+e1^2*(21637-35295*ur1^2+2149*ur1^4)))))*ΔQ^4)/(6*r1^3*(a^2+r1*(-2*M+r1))^6)+((-4*a^11*e1*l1*(59*M+3*(-1+e1^2)*r1)+2*a^12*(71*M+3*(-2+5*e1^2)*r1)-4*a^9*e1*l1*r1*(-3*l1^2-364*M^2+M*r1*(468-33*ur1^2)+3*r1^2*(-11+11*e1^2-ur1^2))-4*a^7*e1*l1*r1^2*(755*M^3-10*l1^2*(8*M+3*r1)+6*r1^3*(-26+26*e1^2-5*ur1^2)+2*M^2*r1*(-1058+205*ur1^2)+M*r1^2*(1987-397*ur1^2-576*ur1^4))-4*a^5*e1*l1*r1^3*(-540*M^4+M^3*r1*(3539-1241*ur1^2)+42*r1^4*(-10+10*e1^2-3*ur1^2)+4*M^2*r1^2*(-1459+554*ur1^2+611*ur1^4)-M*r1^3*(-5511+1999*ur1^2+1590*ur1^4+420*ur1^6)+6*l1^2*(16*M^2-21*r1^2-2*M*r1*(33+56*ur1^2)))-4*a^3*e1*l1*r1^4*(28*M^5+42*r1^5*(-17+17*e1^2-7*ur1^2)+14*M^4*r1*(-168+79*ur1^2)+M^3*r1^2*(6657-4148*ur1^2-2584*ur1^4)+2*M^2*r1^3*(-5028+2583*ur1^2+2180*ur1^4+420*ur1^6)-M*r1^4*(-10146+5225*ur1^2+1376*ur1^4+756*ur1^6)+2*l1^2*(32*M^3-147*r1^3+4*M^2*r1*(20+111*ur1^2)+M*r1^2*(-610-888*ur1^2+105*ur1^4)))-4*a*e1*l1*r1^5*(-2*l1^2*(64*M^4+210*r1^4+8*M^3*r1*(-25+18*ur1^2)+2*M^2*r1^2*(-122-138*ur1^2+105*ur1^4)+M*r1^3*(1312+684*ur1^2-525*ur1^4-210*ur1^6))+r1*(564*M^5+420*r1^5*(-1+e1^2-ur1^2)+2*M^4*r1*(-1286+72*e1^2+1083*ur1^2)-M^3*r1^2*(-7005+312*e1^2+4255*ur1^2+2064*ur1^4)-2*M*r1^4*(-5978+225*e1^2+3820*ur1^2+133*ur1^4+168*ur1^6)+2*M^2*r1^3*(-5431+210*e1^2+3256*ur1^2+906*ur1^4+336*ur1^6)))+a^10*(4*l1^2*(59*M+(2-5*e1^2)*r1)+r1*(-1076*M^2+M*r1*(876-8*ur1^2)+r1^2*(-321+32*ur1^2+e1^2*(379-62*ur1^2))))+a^8*r1*(20*l1^4-l1^2*(1456*M^2+4*M*r1*(-340+33*ur1^2)+r1^2*(175-424*ur1^2+4*e1^2*(41+75*ur1^2)))+r1*(2930*M^3+2*M^2*r1*(-2509+276*ur1^2)+2*M*r1^2*(2008-158*ur1^2+73*ur1^4)+r1^3*(-2125+408*ur1^2+40*ur1^4+e1^2*(2103-701*ur1^2+4*ur1^4))))+a^6*r1^2*(-4*l1^4*(80*M-3*r1*(12+25*ur1^2))+l1^2*(3020*M^3+2*M^2*r1*(-3361+820*ur1^2)-6*M*r1^2*(-983+592*ur1^2+384*ur1^4)+r1^3*(-1100+2571*ur1^2+332*ur1^4-12*e1^2*(66+137*ur1^2)))+r1*(-3228*M^4+2*M^3*r1*(5165-1532*ur1^2)-2*M^2*r1^2*(7559-1424*ur1^2+142*ur1^4)+2*M*r1^3*(6761-1602*ur1^2+90*ur1^4+148*ur1^6)+r1^4*(-7010+1687*ur1^2+609*ur1^4-4*ur1^6+e1^2*(6784-3377*ur1^2+40*ur1^4))))+a^4*r1^3*(24*l1^4*(2*M-r1)*(8*M-r1*(27+56*ur1^2))+r1*(824*M^5+16*M^4*r1*(-525+361*ur1^2)-2*M^3*r1^2*(-11955+4116*ur1^2+281*ur1^4)+2*M*r1^4*(14362-5050*ur1^2-1183*ur1^4+332*ur1^6)-2*M^2*r1^3*(16157-5228*ur1^2-53*ur1^4+368*ur1^6)+r1^5*(-14368+3931*ur1^2+2650*ur1^4-60*ur1^6+e1^2*(14132-9057*ur1^2+156*ur1^4)))-2*l1^2*(1080*M^4+2*M^3*r1*(-2997+1241*ur1^2)+M^2*r1^2*(9579-5387*ur1^2-4888*ur1^4)+M*r1^3*(-7721+7151*ur1^2+2668*ur1^4+840*ur1^6)+2*r1^4*(644-1745*ur1^2-255*ur1^4+105*ur1^6+e1^2*(658+891*ur1^2-105*ur1^4-105*ur1^6))))+2*r1^5*(-2*l1^4*(2*M-r1)*(64*M^3+8*M^2*r1*(-7+18*ur1^2)+10*M*r1^2*(-34-21*ur1^2+21*ur1^4)+15*r1^3*(64+24*ur1^2-21*ur1^4-14*ur1^6))+r1^3*(2064*M^5+8*M^4*r1*(-809+147*e1^2+247*ur1^2)+4*M^3*r1^2*(2850-1291*ur1^2-304*ur1^4+e1^2*(-739+429*ur1^2))+M*r1^4*(16053-7189*ur1^2-3828*ur1^4+108*ur1^6+e1^2*(-5293+4260*ur1^2-96*ur1^4))+2*M^2*r1^3*(-7431+3521*ur1^2+1415*ur1^4-72*ur1^6+e1^2*(2235-1748*ur1^2+36*ur1^4))+r1^5*(-5396-1219*ur1^2+4097*ur1^4-80*ur1^6+e1^2*(5400-4209*ur1^2+92*ur1^4)))+l1^2*r1*(1640*M^5+4*M^4*r1*(-1387+168*e1^2+385*ur1^2)-2*M^3*r1^2*(-5213+2844*ur1^2-606*ur1^4+24*e1^2*(25+13*ur1^2))+M^2*r1^3*(-12865+10715*ur1^2-1926*ur1^4-1344*ur1^6+8*e1^2*(85+42*ur1^2+105*ur1^4))+M*r1^4*(11321-14570*ur1^2+1860*ur1^4+1932*ur1^6+420*ur1^8+e1^2*(580+264*ur1^2-840*ur1^4-420*ur1^6))+r1^5*(-3452+6789*ur1^2-18*ur1^4-1050*ur1^6-420*ur1^8+30*e1^2*(-64-24*ur1^2+21*ur1^4+14*ur1^6))))+a^2*r1^4*(4*l1^4*(64*M^3+8*M^2*r1*(26+111*ur1^2)+2*M*r1^2*(-556-777*ur1^2+105*ur1^4)+r1^3*(496+555*ur1^2-105*ur1^4-105*ur1^6))+r1*(496*M^6-8*M^5*r1*(-249+448*ur1^2)+4*M^4*r1^2*(-4129+1744*ur1^2+273*ur1^4)+2*M^2*r1^4*(-20961+9008*ur1^2+2237*ur1^4-432*ur1^6)+2*M^3*r1^3*(17027-6620*ur1^2-599*ur1^4+144*ur1^6)+4*M*r1^5*(10001-4383*ur1^2-1705*ur1^4+152*ur1^6)+r1^6*(-19966+5475*ur1^2+6015*ur1^4-120*ur1^6+e1^2*(19902-14737*ur1^2+304*ur1^4)))+l1^2*(112*M^5+8*M^4*r1*(-1157+553*ur1^2)-4*M^3*r1^2*(-6043+3189*ur1^2+2584*ur1^4)+2*M*r1^4*(11507-13227*ur1^2-888*ur1^4+252*ur1^6)+2*M^2*r1^3*(-15095+11328*ur1^2+4354*ur1^4+1680*ur1^6)+r1^5*(-3270+11771*ur1^2+484*ur1^4-1680*ur1^6-420*ur1^8+4*e1^2*(-1456-915*ur1^2+420*ur1^4+315*ur1^6)))))*ΔQ^2*Δθ^2)/(8*(a^2+r1*(-2*M+r1))^6)+(r1^3*(-9*a^10*(-3+2*e1^2)+96*a^7*e1*l1*M*r1+12*a^5*e1*l1*M*r1^2*(24*M+r1*(-58+31*ur1^2))-12*a^3*e1*l1*M*r1^3*(96*M^2+4*M*r1*(-78+ur1^2)+r1^2*(354-2*ur1^2+85*ur1^4))+12*a*e1*l1*M*r1^4*(80*M^3-36*M^2*r1*(12+ur1^2)+4*M*r1^2*(180+43*ur1^2+25*ur1^4)-r1^3*(718+177*ur1^2+250*ur1^4+35*ur1^6))+a^8*(18*l1^2+r1*(-84*M+r1*(50+132*ur1^2-15*e1^2*(3+4*ur1^2))))+a^6*r1*(l1^2*(-96*M+3*r1*(9+20*ur1^2))+r1*(-339*M^2+4*M*r1*(125-99*ur1^2)+r1^2*(-325+377*ur1^2-18*ur1^4+3*e1^2*(82-76*ur1^2+35*ur1^4))))-a^4*r1^2*(3*l1^2*(96*M^2+2*M*r1*(-115+62*ur1^2)+7*r1^2*(13-8*ur1^2+5*ur1^4))+r1*(-1848*M^3+3*M^2*r1*(1193+246*ur1^2)-6*M*r1^2*(536+48*ur1^2+127*ur1^4)+r1^3*(1605+135*ur1^2+389*ur1^4+228*ur1^6-3*e1^2*(490-48*ur1^2+208*ur1^4+35*ur1^6))))+r1^4*(-3*l1^2*(2*M-r1)*(160*M^3-4*M^2*r1*(145+18*ur1^2)+4*M*r1^2*(202+55*ur1^2+50*ur1^4)-r1^3*(735+192*ur1^2+303*ur1^4+70*ur1^6))+r1*(1392*M^5+4*M^4*r1*(-1009+228*e1^2-717*ur1^2)+2*M^3*r1^2*(3256+2881*ur1^2+1395*ur1^4-48*e1^2*(21+8*ur1^2))+M^2*r1^3*(-7521-6180*ur1^2-4355*ur1^4-1272*ur1^6+24*e1^2*(108+44*ur1^2+31*ur1^4))+2*M*r1^4*(3478+2463*ur1^2+1951*ur1^4+815*ur1^6+105*ur1^8-3*e1^2*(430+148*ur1^2+165*ur1^4+35*ur1^6))+r1^5*(-2203-2827*ur1^2-1511*ur1^4-1097*ur1^6-210*ur1^8+3*e1^2*(735+192*ur1^2+303*ur1^4+70*ur1^6))))+a^2*r1^3*(3*l1^2*(384*M^3+4*M^2*r1*(-273+4*ur1^2)+4*M*r1^2*(312+2*ur1^2+85*ur1^4)-r1^3*(399+8*ur1^2+173*ur1^4+35*ur1^6))+r1*(-2796*M^4+2*M^3*r1*(3388+1719*ur1^2)-3*M^2*r1^2*(2779+1638*ur1^2+949*ur1^4)+2*M*r1^3*(3504+1755*ur1^2+1534*ur1^4+546*ur1^6)+r1^4*(-3460-1917*ur1^2-1438*ur1^4-830*ur1^6-105*ur1^8+3*e1^2*(1134+200*ur1^2+476*ur1^4+105*ur1^6)))))*Δθ^4)/(48*(a^2+r1*(-2*M+r1))^6))+Δr^4*((ur1*(-8*a^13*e1*M*(29*M^2+71*M*r1+33*r1^2)+a^12*l1*(232*M^3+1688*M^2*r1+508*M*r1^2-67*(-1+e1^2)*r1^3)+a^10*l1*r1*(-288*M^4+4828*M^2*r1^2+l1^2*(2880*M^2+1838*M*r1+(-35+102*e1^2)*r1^2)-16*M^3*r1*(596+189*ur1^2)+4*M*r1^3*(342+191*ur1^2)+r1^4*(1011+29*ur1^2+e1^2*(-1005+38*ur1^2)))+4*a^11*e1*r1*(-(l1^2*(720*M^2+227*M*r1-9*(-1+e1^2)*r1^2))+2*M*(36*M^3+r1^3*(-202+99*ur1^2)+3*M^2*r1*(115+126*ur1^2)+M*r1^2*(-56+355*ur1^2)))+2*a^8*l1*r1^2*(-576*M^5+3*l1^4*(348*M+(18-35*e1^2)*r1)+2*M^4*r1*(5339+3252*ur1^2)+2*M^2*r1^3*(1893-1407*ur1^2+610*ur1^4)+M*r1^4*(-2103+1195*ur1^2+1490*ur1^4)-M^3*r1^2*(16197+6340*ur1^2+1652*ur1^4)+r1^5*(3444+195*ur1^2-19*ur1^4+e1^2*(-3216+247*ur1^2))+l1^2*(-5316*M^3+r1^3*(-221+723*e1^2-70*ur1^2)-8*M^2*r1*(-125+229*ur1^2)+M*r1^2*(2415+1504*ur1^2)))-4*a*e1*r1^6*(42*l1^6*M*(4*M^2+r1^2*(19-70*ur1^2)+2*M*r1*(-13+14*ur1^2))+l1^2*r1^3*(13740*M^4+6*M^3*r1*(-4479+324*e1^2-356*ur1^2)-2763*r1^4*(-1+e1^2-ur1^2)+M*r1^3*(-46519+3078*e1^2+2799*ur1^2-1470*ur1^4)-6*M^2*r1^2*(-6666+486*e1^2-25*ur1^2-490*ur1^4))-3*M*(2*M-r1)*r1^5*(266*M^2+2*M*r1*(-152+155*ur1^2)+r1^2*(93-175*ur1^2-60*ur1^4))+3*l1^4*r1*(880*M^4+921*r1^4+16*M^3*r1*(51-35*ur1^2)+10*M*r1^3*(1095+28*ur1^2-42*ur1^4)+56*M^2*r1^2*(-112-5*ur1^2+15*ur1^4)))+4*a^9*e1*r1^2*(-9*l1^4*(58*M+r1)+l1^2*(2658*M^3+9*r1^3*(-14+14*e1^2-ur1^2)+4*M^2*r1*(-609+229*ur1^2)+2*M*r1^2*(-111+242*ur1^2))+M*(288*M^4-12*M^3*r1*(168+271*ur1^2)+r1^4*(-989+1006*ur1^2+240*ur1^4)+2*M^2*r1^2*(927-313*ur1^2+413*ur1^4)+2*M*r1^3*(1016+863*ur1^2+450*ur1^4)))+4*a^3*e1*r1^5*(-84*l1^6*M*(3*M-2*r1*(3+11*ur1^2))-3*l1^4*(240*M^4+579*r1^4-280*M^3*r1*(-1+ur1^2)+10*M*r1^3*(603+91*ur1^2-112*ur1^4)+8*M^2*r1^2*(-428-105*ur1^2+175*ur1^4))-M*r1^3*(1608*M^4+4*M^3*r1*(-1235+417*ur1^2)+r1^4*(1010-1697*ur1^2-850*ur1^4)+2*M*r1^3*(-2225+2384*ur1^2+274*ur1^4)+2*M^2*r1^2*(3509-1911*ur1^2+792*ur1^4))-l1^2*r1*(192*M^5+12*M^4*r1*(761-506*ur1^2)+9*r1^5*(500-500*e1^2+193*ur1^2)+M*r1^4*(-39153+712*ur1^2-5040*ur1^4)+6*M^2*r1^3*(6608+901*ur1^2+700*ur1^4)+4*M^3*r1^2*(-8134-743*ur1^2+1470*ur1^4)))+4*a^7*e1*r1^3*(3*l1^4*(632*M^2-39*r1^2-10*M*r1*(79+35*ur1^2))-M*(400*M^5-8*M^4*r1*(373+435*ur1^2)+r1^5*(1482-2065*ur1^2-942*ur1^4)+2*M^2*r1^3*(1660+2095*ur1^2+244*ur1^4)+4*M^3*r1^2*(1263+835*ur1^2+413*ur1^4)-2*M*r1^4*(2671-323*ur1^2+1028*ur1^4))+l1^2*(-2100*M^4+M^3*r1*(9096-6172*ur1^2)+9*r1^4*(-82+82*e1^2-13*ur1^2)+2*M^2*r1^2*(-3117-400*ur1^2+2100*ur1^4)+M*r1^3*(4429+1668*ur1^2+2100*ur1^4)))+4*a^5*e1*r1^4*(378*l1^6*M-3*l1^4*(448*M^3+207*r1^3-4*M^2*r1*(461+140*ur1^2)+2*M*r1^2*(1149+490*ur1^2-350*ur1^4))+M*r1*(-1392*M^5+8*M^4*r1*(496+381*ur1^2)+4*M^3*r1^2*(587+321*ur1^2-243*ur1^4)+2*M*r1^4*(3160-2225*ur1^2+512*ur1^4)+r1^5*(-1562+2429*ur1^2+1372*ur1^4)-2*M^2*r1^3*(4411-157*ur1^2+1393*ur1^4))+l1^2*(-672*M^5+9*r1^5*(-262+262*e1^2-69*ur1^2)+4*M^4*r1*(-1661+2170*ur1^2)-40*M^3*r1^2*(-415+147*ur1^2+210*ur1^4)+2*M^2*r1^3*(-10779-3080*ur1^2+1470*ur1^4)+M*r1^4*(18829+1651*ur1^2+5670*ur1^4)))+2*a^6*l1*r1^3*(105*l1^6+800*M^6-48*M^5*r1*(212+145*ur1^2)+2*M^4*r1^2*(14816+10135*ur1^2+1652*ur1^4)-M^3*r1^3*(22775+1373*ur1^2+11472*ur1^4)+2*M*r1^5*(-9118-54*ur1^2+2639*ur1^4+525*ur1^6)+M^2*r1^4*(11667-6928*ur1^2-5916*ur1^4+2100*ur1^6)+r1^6*(12076+1379*ur1^2-228*ur1^4+e1^2*(-11524+1311*ur1^2))+l1^2*(4200*M^4+r1^4*(-1105+4359*e1^2-882*ur1^2)+2*M*r1^3*(-458+1841*ur1^2)+M^3*r1*(-9301+12344*ur1^2)-4*M^2*r1^2*(-116+2963*ur1^2+2100*ur1^4))-3*l1^4*(1264*M^2-2*M*r1*(571+350*ur1^2)+r1^2*(53-245*ur1^2+7*e1^2*(23+30*ur1^2))))+2*l1*r1^6*(42*l1^6*(2*M-r1)*(4*M^2+2*r1^2*(5-21*ur1^2)+M*r1*(-15+28*ur1^2))+l1^2*r1^3*(14244*M^4+r1^4*(-952+20265*e1^2-23508*ur1^2)-36*M^3*r1*(782+8*e1^2+33*ur1^2)+3*M^2*r1^2*(7153+988*e1^2-1764*ur1^2+980*ur1^4)-M*r1^3*(3568+12030*e1^2-20049*ur1^2+1470*ur1^4))+3*l1^4*r1*(332*M^4-2*M^3*r1*(-893+196*e1^2+476*ur1^2)+4*M^2*r1^2*(-2419+420*ur1^2+252*ur1^4+14*e1^2*(8+ur1^2))+r1^4*(-6943+448*ur1^2+588*ur1^4-28*e1^2*(-5+21*ur1^2))+4*M*r1^3*(4559-399*ur1^2-224*ur1^4+e1^2*(-77+91*ur1^2)))+r1^5*(13728*M^4+6*M^3*r1*(-5729+1206*e1^2-797*ur1^2)+3*M^2*r1^2*(16713+2817*ur1^2-608*ur1^4+36*e1^2*(-134+19*ur1^2))+M*r1^3*(-57226-9978*ur1^2+2844*ur1^4-9*e1^2*(-2077+342*ur1^2))+r1^4*(19517+16472*ur1^2-3189*ur1^4+e1^2*(-19631+3249*ur1^2))))+2*a^4*l1*r1^4*(-126*l1^6*(6*M-r1*(3+5*ur1^2))+l1^2*(1344*M^5+r1^5*(-5473+14847*e1^2-4563*ur1^2)+4*M^4*r1*(2243-4340*ur1^2)+M^2*r1^3*(16173-14252*ur1^2-18060*ur1^4)+6*M^3*r1^2*(-2097+5213*ur1^2+2800*ur1^4)+2*M*r1^4*(-5956+2584*ur1^2-735*ur1^4+1050*ur1^6))+3*l1^4*(896*M^3-2*M^2*r1*(1363+560*ur1^2)+2*M*r1^2*(1566+91*ur1^2-700*ur1^4)+r1^3*(-932+952*ur1^2+210*ur1^4-7*e1^2*(33+118*ur1^2)))+r1*(2760*M^6-4*M^5*r1*(4217+3567*ur1^2)+M^2*r1^4*(42567-1483*ur1^2-18508*ur1^4)+2*M^4*r1^2*(14117+4212*ur1^2+7380*ur1^4)+M^3*r1^3*(-24953+7036*ur1^2+932*ur1^4-4200*ur1^6)+M*r1^5*(-48537-5480*ur1^2+6776*ur1^4+2100*ur1^6)+r1^6*(25845+5167*ur1^2-1137*ur1^4+e1^2*(-25527+3667*ur1^2))))+2*a^2*l1*r1^5*(21*l1^6*(2*M-r1)*(12*M-r1*(15+88*ur1^2))-l1^2*r1*(3012*M^5+12*M^4*r1*(-837+1429*ur1^2)+r1^5*(14870-31425*e1^2+13549*ur1^2)-3*M^3*r1^2*(-10435+5018*ur1^2+6440*ur1^4)+M*r1^4*(11481-11291*ur1^2+2940*ur1^4-2100*ur1^6)+2*M^2*r1^3*(-18085+2661*ur1^2+3360*ur1^4+2100*ur1^6))+3*l1^4*(480*M^4+M^3*r1*(822-560*ur1^2)-2*M*r1^3*(-4763+987*ur1^2+1162*ur1^4)+2*M^2*r1^2*(-2393+406*ur1^2+1400*ur1^4)+r1^4*(-3747+1309*ur1^2+616*ur1^4-7*e1^2*(-5+172*ur1^2)))+r1^3*(-6876*M^5-6*M^4*r1*(-2280+431*ur1^2)+3*M^3*r1^2*(-14423+165*ur1^2+4568*ur1^4)+M^2*r1^3*(68783+9252*ur1^2-12144*ur1^4-2100*ur1^6)+M*r1^4*(-71367-10379*ur1^2+5034*ur1^4+1050*ur1^6)+r1^5*(36258+11094*ur1^2-2578*ur1^4+e1^2*(-36381+5833*ur1^2)))))*ΔQ^4*ΔR)/(6*r1^4*(a^2+r1*(-2*M+r1))^5)+(ur1*(2*a^10*l1*(-248*M^2+117*M*r1+3*(47-44*e1^2)*r1^2)-2*a^11*e1*(-248*M^2+162*M*r1+9*(-1+e1^2)*r1^2)+2*a^9*e1*r1*(-1836*M^3+9*l1^2*(-16*M+r1)+9*r1^3*(14-14*e1^2+ur1^2)+12*M^2*r1*(255+146*ur1^2)+2*M*r1^2*(-604+537*ur1^2))+a^8*l1*r1*(3672*M^3+6*l1^2*(48*M+(101-54*e1^2)*r1)-16*M^2*r1*(256+219*ur1^2)-6*M*r1^2*(205+333*ur1^2)+3*r1^3*(1225+66*ur1^2+e1^2*(-1081+4*ur1^2)))+a^6*l1*r1^2*(324*l1^4-8256*M^4+2*M^3*r1*(8729+7692*ur1^2)-12*M*r1^3*(1821+875*ur1^2+18*ur1^4)-2*M^2*r1^2*(2023-2218*ur1^2+2176*ur1^4)+3*r1^4*(6011+883*ur1^2-4*ur1^4+e1^2*(-5677+40*ur1^2))+3*l1^2*(856*M^2+r1^2*(1553-452*e1^2+116*ur1^2)-16*M*r1*(166+143*ur1^2)))+2*a^7*e1*r1^2*(4128*M^4+9*r1^4*(82-82*e1^2+13*ur1^2)-12*M^3*r1*(1181+641*ur1^2)+4*M*r1^3*(-1058+1044*ur1^2+267*ur1^4)+4*M^2*r1^2*(2877-168*ur1^2+544*ur1^4)+3*l1^2*(-428*M^2+39*r1^2+4*M*r1*(241+286*ur1^2)))-2*a^5*e1*r1^3*(-1032*l1^4*M+2896*M^5+9*r1^5*(-262+262*e1^2-69*ur1^2)-24*M^4*r1*(980+349*ur1^2)-4*M^2*r1^3*(5623-2535*ur1^2+460*ur1^4)+4*M^3*r1^2*(7767+1194*ur1^2+1088*ur1^4)-2*M*r1^4*(-4508+3209*ur1^2+1468*ur1^4)-3*l1^2*(2252*M^3+207*r1^3-4*M^2*r1*(1481+1378*ur1^2)+4*M*r1^2*(1726+802*ur1^2+525*ur1^4)))+6*a*e1*r1^5*(r1^3*(3424*M^4-921*r1^4*(-1+e1^2-ur1^2)+8*M^3*r1*(-755+81*e1^2+229*ur1^2)+2*M*r1^3*(-1614+513*e1^2-157*ur1^2+120*ur1^4)-4*M^2*r1^2*(-1234+243*e1^2+423*ur1^2+120*ur1^4))-8*l1^4*M*(44*M^2-10*M*r1*(23+14*ur1^2)+r1^2*(209+350*ur1^2+175*ur1^4))+l1^2*r1*(-7128*M^4+921*r1^4+4*M^3*r1*(3661+1404*ur1^2)+4*M*r1^3*(8171+164*ur1^2+420*ur1^4)-4*M^2*r1^2*(6287+1154*ur1^2+840*ur1^4)))-2*a^3*e1*r1^4*(240*l1^4*M*(M+r1*(-2+7*ur1^2))+r1*(12720*M^5+9*r1^5*(-500+500*e1^2-193*ur1^2)-152*M^4*r1*(164+15*ur1^2)+4*M^2*r1^3*(-6422+3341*ur1^2+484*ur1^4)-4*M*r1^4*(-3109+958*ur1^2+647*ur1^4)+4*M^3*r1^2*(8399-1527*ur1^2+900*ur1^4))+3*l1^2*(2408*M^4-579*r1^4-208*M^3*r1*(59+31*ur1^2)+12*M^2*r1^2*(1465+848*ur1^2+350*ur1^4)-4*M*r1^3*(5069+728*ur1^2+945*ur1^4)))-a^4*l1*r1^3*(-5792*M^5+1032*l1^4*(2*M-r1)+8*M^4*r1*(3203+2094*ur1^2)+6*M*r1^4*(13343+4493*ur1^2+196*ur1^4)+2*M^2*r1^3*(-23528-17263*ur1^2+2920*ur1^4)-2*M^3*r1^2*(9722-2903*ur1^2+4352*ur1^4)-3*r1^5*(16809+4540*ur1^2-108*ur1^4+3*e1^2*(-5567+52*ur1^2))+6*l1^2*(2252*M^3-M^2*r1*(5997+5512*ur1^2)+M*r1^2*(7619+2600*ur1^2+2100*ur1^4)+r1^3*(-2623+104*ur1^2+350*ur1^4+e1^2*(222-280*ur1^2-350*ur1^4))))+3*a^2*l1*r1^4*(20*l1^4*(8*M^2+14*M*r1*(-1+4*ur1^2)+r1^2*(5-28*ur1^2-35*ur1^4))+r1*(3800*M^5+4*M^4*r1*(-1392+1049*ur1^2)+2*M^2*r1^3*(20627+8953*ur1^2+8*ur1^4)-2*M*r1^4*(25529+7594*ur1^2+104*ur1^4)+2*M^3*r1^2*(-8441-5839*ur1^2+640*ur1^4)+r1^5*(29921+11873*ur1^2-136*ur1^4+e1^2*(-30161+304*ur1^2)))+l1^2*(4816*M^4-8*M^3*r1*(2519+1612*ur1^2)+12*M^2*r1^2*(2745+1009*ur1^2+700*ur1^4)-2*M*r1^3*(17517+248*ur1^2+980*ur1^4)+r1^4*(11085-2244*ur1^2-2660*ur1^4-700*ur1^6+20*e1^2*(39+112*ur1^2+105*ur1^4))))+6*l1*r1^5*(4*l1^4*(2*M-r1)*(44*M^2-M*r1*(137+140*ur1^2)+5*r1^2*(22+42*ur1^2+35*ur1^4))+2*r1^3*(2212*M^4+2*M^3*r1*(-2978+615*e1^2-854*ur1^2)+2*r1^4*(2249+2257*ur1^2-16*ur1^4+e1^2*(-2268+23*ur1^2))+M^2*r1^2*(9923+3237*ur1^2+40*ur1^4+e1^2*(-2686+36*ur1^2))-M*r1^3*(12745+4039*ur1^2+18*ur1^4+e1^2*(-3927+48*ur1^2)))+l1^2*r1*(4444*M^4-4*M^3*r1*(2871+196*e1^2+71*ur1^2)+M^2*r1^2*(18451-1130*ur1^2-840*ur1^4+160*e1^2*(6+7*ur1^2))+4*r1^4*(2137-345*ur1^2-385*ur1^4-175*ur1^6+5*e1^2*(22+42*ur1^2+35*ur1^4))-2*M*r1^3*(12003-1488*ur1^2-1190*ur1^4-350*ur1^6+e1^2*(372+560*ur1^2+350*ur1^4)))))*ΔQ^2*ΔR*Δθ^2)/(24*r1*(a^2+r1*(-2*M+r1))^5)-(r1^2*ur1*(-3*a^8*l1*(12*M+11*(5-2*e1^2)*r1)-18*a^9*e1*(-2*M+(-1+e1^2)*r1)-6*a^7*e1*r1*(-3*l1^2+46*M^2+4*M*r1*(-11+42*ur1^2)+3*r1^2*(-9-2*ur1^2+e1^2*(9+ur1^2)))-6*a^5*e1*r1^2*(-122*M^3+M^2*r1*(334-694*ur1^2)+2*M*r1^2*(-7+274*ur1^2+47*ur1^4)-l1^2*(8*M+3*r1*(8+ur1^2))-3*r1^3*(33+15*ur1^2+ur1^4-e1^2*(33+7*ur1^2)))-3*a^6*l1*r1*(22*l1^2-92*M^2-2*M*r1*(65+168*ur1^2)+r1^2*(65-75*ur1^2+e1^2*(-5+112*ur1^2)))-6*a^3*e1*r1^3*(108*M^4+4*M^3*r1*(-168+179*ur1^2)+2*M*r1^3*(96+360*ur1^2+89*ur1^4)-2*M^2*r1^2*(-195+738*ur1^2+94*ur1^4)+3*r1^4*(-65-43*ur1^2-6*ur1^4+e1^2*(65+18*ur1^2))+l1^2*(224*M^2-3*r1^2*(25+6*ur1^2)-4*M*r1*(154+145*ur1^2)))+a^4*l1*r1^2*(-732*M^3+3*M^2*r1*(511-1388*ur1^2)+l1^2*(-48*M+51*r1+336*r1*ur1^2)+12*M*r1^2*(-124+ur1^2+47*ur1^4)+r1^3*(1443+2029*ur1^2+915*ur1^4-3*e1^2*(474+701*ur1^2+175*ur1^4)))+a^2*l1*r1^3*(648*M^4+6*M^3*r1*(-867+716*ur1^2)+3*M^2*r1^2*(2668+413*ur1^2-376*ur1^4)-2*M*r1^3*(4164+3845*ur1^2+1698*ur1^4)+3*l1^2*(448*M^2-2*M*r1*(569+580*ur1^2)+r1^2*(457+589*ur1^2+175*ur1^4))+r1^4*(5241+6293*ur1^2+3322*ur1^4+525*ur1^6-3*e1^2*(1675+1702*ur1^2+525*ur1^4)))+12*a*e1*r1^4*(l1^2*(144*M^3+6*r1^3*(10+3*ur1^2)-8*M^2*r1*(85+43*ur1^2)+7*M*r1^2*(144+128*ur1^2+25*ur1^4))+r1*(-194*M^4+M^3*r1*(239+36*e1^2-382*ur1^2)-6*r1^4*(-1+e1^2-ur1^2)*(10+3*ur1^2)+M^2*r1^2*(-11+471*ur1^2+78*ur1^4-6*e1^2*(10+3*ur1^2))+M*r1^3*(-150-221*ur1^2-51*ur1^4+3*e1^2*(22+7*ur1^2))))+l1*r1^4*(-3*l1^2*(2*M-r1)*(288*M^2-4*M*r1*(233+172*ur1^2)+7*r1^2*(174+159*ur1^2+50*ur1^4))+r1*(3672*M^4+6*M^3*r1*(-1371+244*e1^2-765*ur1^2)+M^2*r1^2*(10671+9247*ur1^2+4260*ur1^4-12*e1^2*(203+199*ur1^2))+r1^4*(3768+6889*ur1^2+4315*ur1^4+1050*ur1^6-21*e1^2*(174+159*ur1^2+50*ur1^4))+2*M*r1^3*(-5637-6155*ur1^2-3100*ur1^4-525*ur1^6+3*e1^2*(536+552*ur1^2+175*ur1^4)))))*ΔR*Δθ^4)/(48*(a^2+r1*(-2*M+r1))^5))+Δr^3*((4*(-4*a^13*e1*l1*M^2*(61*M+39*r1)+a^14*M^2*(116*M+75*r1)+a^12*(l1^2*(244*M^3+331*M^2*r1-2*M*r1^2-(-1+e1^2)*r1^3)+M*r1*(-402*M^3+10*M*r1^2*(61-3*ur1^2)-6*r1^3*(3+4*ur1^2)+M^2*r1*(465+46*ur1^2)))+2*a^11*e1*l1*r1*(l1^2*(-190*M^2+8*M*r1+3*(-1+e1^2)*r1^2)+2*M*(132*M^3+6*r1^3*(5+6*ur1^2)+M*r1^2*(-226+203*ur1^2)+M^2*r1*(-207+296*ur1^2)))-2*a*e1*l1*r1^6*(42*l1^6*M*(4*M^2+r1^2*(19-10*ur1^2)+4*M*r1*(-4+ur1^2))+l1^2*r1^3*(4008*M^4-921*r1^4*(-1+e1^2-ur1^2)+12*M^3*r1*(-485+54*e1^2+110*ur1^2)+M*r1^3*(-4043+1026*e1^2+4125*ur1^2-1260*ur1^4)-6*M^2*r1^2*(-793+162*e1^2+549*ur1^2-420*ur1^4))+3*l1^4*r1*(312*M^4+307*r1^4-140*M^3*r1*(-3+4*ur1^2)+2*M*r1^3*(2413+77*ur1^2-98*ur1^4)+4*M^2*r1^2*(-716-7*ur1^2+98*ur1^4))+3*M*(2*M-r1)*r1^5*(192*M^2-2*M*r1*(70+29*ur1^2)+r1^2*(19+75*ur1^2+166*ur1^4)))+2*a^9*e1*l1*r1^2*(-3*l1^4*(24*M+r1)+l1^2*(402*M^3+3*r1^3*(-14+14*e1^2-ur1^2)-4*M*r1^2*(-76+93*ur1^2)-2*M^2*r1*(597+226*ur1^2))+M*(360*M^4-4*M^3*r1*(-390+799*ur1^2)+r1^4*(323+272*ur1^2+720*ur1^4)+2*M^2*r1^2*(96-121*ur1^2+1253*ur1^4)+2*M*r1^3*(-728+483*ur1^2+1356*ur1^4)))+2*a^3*e1*l1*r1^5*(168*l1^6*M*(M+r1*(-2+3*ur1^2))-3*l1^4*(248*M^4+193*r1^4-8*M^3*r1*(30+7*ur1^2)+28*M*r1^3*(101+21*ur1^2-22*ur1^4)+4*M^2*r1^2*(-327-140*ur1^2+210*ur1^4))+M*r1^3*(1224*M^4-68*M^3*r1*(58+15*ur1^2)+2*M^2*r1^2*(2513+509*ur1^2-2172*ur1^4)-2*M*r1^3*(1163+466*ur1^2+820*ur1^4)+r1^4*(314+477*ur1^2+2404*ur1^4))-l1^2*r1*(1032*M^5+3*r1^5*(500-500*e1^2+193*ur1^2)-8*M^4*r1*(-496+489*ur1^2)-3*M*r1^4*(1477-1468*ur1^2+1540*ur1^4)+2*M^2*r1^3*(4297-2071*ur1^2+2100*ur1^4)+2*M^3*r1^2*(-5777+494*ur1^2+2520*ur1^4)))+2*a^7*e1*l1*r1^3*(l1^4*(96*M^2-39*r1^2-24*M*r1*(24+35*ur1^2))+l1^2*(624*M^4+M^3*r1*(2946-820*ur1^2)+3*r1^4*(-82+82*e1^2-13*ur1^2)+8*M^2*r1^2*(-510-101*ur1^2+525*ur1^4)+M*r1^3*(1465-1768*ur1^2+2100*ur1^4))+M*(-800*M^5+8*M^4*r1*(-93+503*ur1^2)-2*M^2*r1^3*(-1510+1319*ur1^2+796*ur1^4)-4*M^3*r1^2*(-330+981*ur1^2+1253*ur1^4)+r1^5*(666+355*ur1^2+2772*ur1^4)+2*M*r1^4*(-1563+7*ur1^2+3002*ur1^4)))+2*a^5*e1*l1*r1^4*(-42*l1^6*M+3*l1^4*(156*M^3-69*r1^3+4*M^2*r1*(69+133*ur1^2)+2*M*r1^2*(-475-357*ur1^2+210*ur1^4))+M*r1*(-288*M^5+8*M^4*r1*(-97+489*ur1^2)+14*M*r1^4*(-274-61*ur1^2+200*ur1^4)-4*M^3*r1^2*(640-115*ur1^2+663*ur1^4)+r1^5*(660+407*ur1^2+3958*ur1^4)-2*M^2*r1^3*(-3073+59*ur1^2+4069*ur1^4))+l1^2*(-1336*M^5+3*r1^5*(-262+262*e1^2-69*ur1^2)+8*M^4*r1*(-89+431*ur1^2)+4*M^2*r1^3*(-2079+290*ur1^2+630*ur1^4)-2*M^3*r1^2*(-4111+740*ur1^2+4200*ur1^4)+M*r1^4*(3141-3619*ur1^2+5460*ur1^4)))+a^8*r1^2*(6*l1^6*(24*M-7*r1)+l1^4*(-804*M^3+r1^3*(-478+492*e1^2-57*ur1^2)+30*M*r1^2*(1+58*ur1^2)+4*M^2*r1*(465+226*ur1^2))+r1*(2408*M^6-15*r1^6*(-7+ur1^2)+4*M^5*r1*(1233+346*ur1^2)-2*M^4*r1^2*(1128+1088*ur1^2+2033*ur1^4)+6*M*r1^5*(10-41*ur1^2+203*ur1^4+40*ur1^6)+2*M^2*r1^4*(1917+158*ur1^2+680*ur1^4+462*ur1^6)+M^3*r1^3*(-7810-448*ur1^2-2227*ur1^4+882*ur1^6))-l1^2*(720*M^5+M^4*r1*(3234-6392*ur1^2)+M*r1^4*(1071-1510*ur1^2-462*ur1^4)+M^2*r1^3*(-6467+3098*ur1^2+2526*ur1^4)+M^3*r1^2*(5769+5105*ur1^2+5012*ur1^4)+r1^5*(-201+181*ur1^2+15*ur1^4+e1^2*(96-195*ur1^2))))+a^10*r1*(l1^4*(380*M^2+56*M*r1+(-41+42*e1^2)*r1^2)+r1*(-324*M^5+30*r1^5-4*M^4*r1*(801+118*ur1^2)+3*M*r1^4*(15-28*ur1^2+88*ur1^4)+4*M^3*r1^2*(-267+122*ur1^2+209*ur1^4)+M^2*r1^3*(2298+200*ur1^2+867*ur1^4))+l1^2*(-528*M^4+M^3*r1*(15-1184*ur1^2)+M^2*r1^2*(1973+65*ur1^2)+4*M*r1^3*(-72+91*ur1^2)+r1^4*(15-14*ur1^2+15*e1^2*(-1+ur1^2))))-a^2*r1^5*(42*l1^8*(2*M-r1)*(4*M+r1*(-5+12*ur1^2))+3*r1^5*(1232*M^5+8*M^4*r1*(-242+57*ur1^2)-4*M^3*r1^2*(-284+37*ur1^2+428*ur1^4)+M*r1^4*(1+85*ur1^2-195*ur1^4-86*ur1^6)+r1^5*(10+11*ur1^2+13*ur1^4-2*ur1^6)+4*M^2*r1^3*(-70-61*ur1^2+304*ur1^4+43*ur1^6))+l1^4*r1*(2448*M^5+24*M^4*r1*(-340+437*ur1^2)+r1^5*(13453-13968*e1^2+7215*ur1^2)-84*M^3*r1^2*(-97+137*ur1^2+180*ur1^4)-3*M*r1^4*(5810+2881*ur1^2-2100*ur1^4+700*ur1^6)+4*M^2*r1^3*(905+1716*ur1^2-210*ur1^4+1050*ur1^6))+l1^2*r1^3*(7632*M^5+24*M^4*r1*(-596+367*ur1^2)-12*M^3*r1^2*(-1095+760*ur1^2+1592*ur1^4)-M*r1^4*(-3042+5872*ur1^2+1317*ur1^4+2100*ur1^6)+2*M^2*r1^3*(-3644+2337*ur1^2+4869*ur1^4+2100*ur1^6)+r1^5*(-1074+3844*ur1^2+2097*ur1^4+e1^2*(1086-4605*ur1^2)))-6*l1^6*(248*M^4+M^3*r1*(44-56*ur1^2)+12*M^2*r1^2*(-111+70*ur1^4)-2*M*r1^3*(-1262+77*ur1^2+329*ur1^4)+r1^4*(-992+91*ur1^2+84*ur1^4-21*e1^2*(-5+6*ur1^2))))+a^4*r1^4*(42*l1^8*(2*M+r1*(-1+5*ur1^2))+3*r1^3*(-536*M^6-4*M^5*r1*(295+102*ur1^2)+r1^6*(10-21*ur1^2+7*ur1^4)+2*M^4*r1^2*(2183+12*ur1^2+733*ur1^4)+M^3*r1^3*(-3253+434*ur1^2+303*ur1^4-676*ur1^6)+2*M^2*r1^4*(423+98*ur1^2-1126*ur1^4-3*ur1^6)+M*r1^5*(-90-163*ur1^2+601*ur1^4+258*ur1^6))+l1^4*(2672*M^5+2*r1^5*(-3457+3702*e1^2-1440*ur1^2)+16*M^4*r1*(317-431*ur1^2)-12*M^2*r1^3*(-355+1041*ur1^2+980*ur1^4)+4*M^3*r1^2*(-3073+3679*ur1^2+4200*ur1^4)+M*r1^4*(6383+6528*ur1^2-6300*ur1^4+2100*ur1^6))-6*l1^6*(156*M^3+4*M^2*r1*(78+133*ur1^2)+2*M*r1^2*(-450-161*ur1^2+210*ur1^4)+r1^3*(373-112*ur1^2-35*ur1^4+7*e1^2*(-6+17*ur1^2)))+l1^2*r1*(-4296*M^6+4*M^5*r1*(23-3369*ur1^2)-4*M^2*r1^4*(-2871+2408*ur1^2+5512*ur1^4)+2*M^4*r1^2*(10225+2134*ur1^2+9798*ur1^4)+M^3*r1^3*(-23071+16811*ur1^2+11522*ur1^4-8400*ur1^6)+M*r1^5*(-3726+3589*ur1^2+1311*ur1^4+4200*ur1^6)+r1^6*(960-2597*ur1^2-909*ur1^4+3*e1^2*(-254+965*ur1^2))))+r1^6*(84*l1^8*(2*M-r1)*(2*M^2+r1^2*(5-3*ur1^2)+M*r1*(-5+2*ur1^2))+l1^4*r1^3*(1584*M^4+r1^4*(-8102+8622*e1^2-11049*ur1^2)-12*M^3*r1*(-57+60*e1^2+50*ur1^2)+M*r1^3*(21295-5748*e1^2+11547*ur1^2-2100*ur1^4)+30*M^2*r1^2*(-364+76*e1^2-117*ur1^2+140*ur1^4))+3*(2*M-r1)*r1^7*(20*M^3-2*M^2*r1*(5+22*ur1^2)+M*r1^2*(-10+23*ur1^2-11*ur1^4)+r1^3*(5+2*ur1^2+11*ur1^4-2*ur1^6))+l1^2*r1^5*(1704*M^4+36*M^3*r1*(-79+6*e1^2+15*ur1^2)+M*r1^3*(-1697+5649*ur1^2+1662*ur1^4+e1^2*(558-2430*ur1^2))+6*M^2*r1^2*(367-458*ur1^2-12*ur1^4+18*e1^2*(-4+15*ur1^2))+r1^4*(547-1817*ur1^2-2568*ur1^4+e1^2*(-586+2565*ur1^2)))-6*l1^6*r1*(16*M^4+8*M^3*r1*(-82+7*e1^2+49*ur1^2)-4*M^2*r1^2*(-596+105*ur1^2+84*ur1^4+21*e1^2*(1+ur1^2))+r1^4*(1515+28*ur1^2-42*ur1^4+14*e1^2*(-5+3*ur1^2))+14*M*r1^3*(e1^2*(6+ur1^2)+2*(-145+5*ur1^2+7*ur1^4))))+a^6*r1^3*(-(l1^4*(1248*M^4-20*M^3*r1*(-291+82*ur1^2)+r1^4*(2279-2508*e1^2+630*ur1^2)+2*M*r1^3*(-572-2529*ur1^2+1050*ur1^4)+4*M^2*r1^2*(-1230+1397*ur1^2+2100*ur1^4)))+r1*(-2160*M^7-48*M^6*r1*(41+26*ur1^2)+3*r1^7*(40-17*ur1^2+9*ur1^4)+4*M^5*r1^2*(1189+672*ur1^2+1197*ur1^4)+4*M^4*r1^3*(2169+128*ur1^2+66*ur1^4-441*ur1^6)+3*M*r1^6*(-70-159*ur1^2+757*ur1^4+252*ur1^6)-2*M^3*r1^4*(6432+112*ur1^2+2785*ur1^4+483*ur1^6)+M^2*r1^5*(3739+212*ur1^2-2441*ur1^4+1458*ur1^6))-6*l1^6*(32*M^2-20*M*r1*(9+14*ur1^2)+r1^2*(82-35*ur1^2+7*e1^2*(-1+5*ur1^2)))+l1^2*(1600*M^6+M^5*r1*(6004-8048*ur1^2)+M^3*r1^3*(-19251+2314*ur1^2-9758*ur1^4)+8*M^4*r1^2*(569+2293*ur1^2+1253*ur1^4)+2*M*r1^5*(-1304+1149*ur1^2+705*ur1^4+1050*ur1^6)+M^2*r1^4*(10791-10257*ur1^2-14110*ur1^4+4200*ur1^6)+r1^6*(e1^2*(-344+1035*ur1^2)-4*(-155+254*ur1^2+45*ur1^4)))))*ΔQ^6)/(3*r1^6*(a^2+r1*(-2*M+r1))^4)+((-2*a^11*e1*l1*(-4*M^2+32*M*r1+9*(-1+e1^2)*r1^2)+a^12*(158*M^2+14*M*r1+13*(-1+e1^2)*r1^2)+2*a^9*e1*l1*r1*(-1188*M^3+9*l1^2*(12*M+r1)+9*r1^3*(14-14*e1^2+ur1^2)+4*M*r1^2*(-82+277*ur1^2)+4*M^2*r1*(84+499*ur1^2))+2*a^7*e1*l1*r1^2*(4608*M^4+9*r1^4*(82-82*e1^2+13*ur1^2)-4*M^3*r1*(1437+2581*ur1^2)+4*M*r1^3*(-655+1119*ur1^2+930*ur1^4)+4*M^2*r1^2*(342-167*ur1^2+1882*ur1^4)-3*l1^2*(568*M^2-39*r1^2-2*M*r1*(317+200*ur1^2)))-2*a^5*e1*l1*r1^3*(156*l1^4*M+4496*M^5+9*r1^5*(-262+262*e1^2-69*ur1^2)-8*M^4*r1*(1904+1583*ur1^2)-4*M^2*r1^3*(1836-2935*ur1^2+1492*ur1^4)-4*M*r1^4*(-2493+2106*ur1^2+2540*ur1^4)+4*M^3*r1^2*(1883+2256*ur1^2+3764*ur1^4)-3*l1^2*(1824*M^3+207*r1^3-8*M^2*r1*(476+361*ur1^2)+4*M*r1^2*(819+356*ur1^2+700*ur1^4)))+2*a*e1*l1*r1^5*(-12*l1^4*M*(68*M^2-6*M*r1*(46+35*ur1^2)+r1^2*(323+525*ur1^2+350*ur1^4))+3*l1^2*r1*(-3840*M^4+921*r1^4+16*M^3*r1*(459+305*ur1^2)+8*M*r1^3*(2080+197*ur1^2+280*ur1^4)-4*M^2*r1^2*(3035+1026*ur1^2+1120*ur1^4))+r1^3*(3648*M^4-2763*r1^4*(-1+e1^2-ur1^2)+24*M^3*r1*(-476+81*e1^2+340*ur1^2)-12*M^2*r1^2*(-1705+243*e1^2+906*ur1^2+424*ur1^4)+2*M*r1^3*(-11722+1539*e1^2+4038*ur1^2+1272*ur1^4)))-2*a^3*e1*l1*r1^4*(12*l1^4*M*(-64*M+r1*(128+105*ur1^2))+r1*(9840*M^5+9*r1^5*(-500+500*e1^2-193*ur1^2)-8*M^4*r1*(1192+897*ur1^2)+28*M^3*r1^2*(373-203*ur1^2+420*ur1^4)+4*M^2*r1^3*(-4559+4507*ur1^2+1750*ur1^4)-4*M*r1^4*(-5190+2473*ur1^2+2246*ur1^4))+3*l1^2*(1664*M^4-579*r1^4-8*M^3*r1*(905+522*ur1^2)+4*M^2*r1^2*(2219+1632*ur1^2+1400*ur1^4)-2*M*r1^3*(4769+1012*ur1^2+2520*ur1^4)))+a^10*(-(l1^2*(8*M^2+44*M*r1+13*(-5+6*e1^2)*r1^2))+r1*(102*M^3+2*M*r1^2*(285-172*ur1^2)+14*M^2*r1*(129-16*ur1^2)+r1^3*(-135+16*ur1^2+e1^2*(195-29*ur1^2))))+a^6*r1^2*(12*l1^6+6*l1^4*(568*M^2+r1^2*(169+24*e1^2+8*ur1^2)-2*M*r1*(309+200*ur1^2))+r1*(11720*M^5+16*M^4*r1*(458-305*ur1^2)-2*M^3*r1^2*(7211+708*ur1^2+1265*ur1^4)+2*M*r1^4*(4250-2994*ur1^2+1079*ur1^4+276*ur1^6)+2*M^2*r1^3*(-1933+5660*ur1^2-1195*ur1^4+570*ur1^6)+r1^5*(-4172+653*ur1^2+456*ur1^4+e1^2*(4472-2001*ur1^2)))-2*l1^2*(4608*M^4-116*M^3*r1*(12+89*ur1^2)+M*r1^3*(3833+7051*ur1^2+3696*ur1^4)+2*M^2*r1^2*(-1377-1064*ur1^2+3764*ur1^4)+r1^4*(-3133-711*ur1^2-18*ur1^4+30*e1^2*(115+6*ur1^2))))+a^8*r1*(-6*l1^4*(36*M+(-15+2*e1^2)*r1)+l1^2*(2376*M^3+8*M^2*r1*(102-499*ur1^2)-10*M*r1^2*(99+254*ur1^2)+r1^3*(1114+143*ur1^2-12*e1^2*(95+3*ur1^2)))+r1*(-4500*M^4+2*M^3*r1*(-3705+934*ur1^2)+2*M^2*r1^2*(1239+782*ur1^2+211*ur1^4)+2*M*r1^3*(1404-1240*ur1^2+265*ur1^4)+r1^4*(-1002+75*ur1^2+29*ur1^4-13*e1^2*(-96+29*ur1^2))))+a^2*r1^4*(-12*l1^6*(128*M^2-14*M*r1*(16+15*ur1^2)+5*r1^2*(16+21*ur1^2+35*ur1^4))+r1^3*(-6048*M^5+48*M^4*r1*(105+158*ur1^2)+24*M^3*r1^2*(537-681*ur1^2+401*ur1^4)+2*M*r1^4*(14202-5740*ur1^2-1803*ur1^4+240*ur1^6)-4*M^2*r1^3*(6697-4356*ur1^2+1056*ur1^4+240*ur1^6)+r1^5*(-14286+2289*ur1^2+3662*ur1^4+36*ur1^6+e1^2*(14118-8903*ur1^2)))+2*l1^2*r1*(1920*M^5+216*M^4*r1*(3+4*ur1^2)+12*M^3*r1^2*(-1061-1481*ur1^2+354*ur1^4)+2*M^2*r1^3*(10175+16125*ur1^2+4854*ur1^4)-M*r1^4*(26253+23183*ur1^2+8100*ur1^4)+r1^5*(19856+12112*ur1^2+441*ur1^4-24*e1^2*(964+57*ur1^2)))+6*l1^4*(1664*M^4-8*M^3*r1*(691+522*ur1^2)-2*M*r1^3*(3789+338*ur1^2+1190*ur1^4)+4*M^2*r1^2*(1841+1187*ur1^2+1400*ur1^4)+r1^4*(2333-848*ur1^2-1260*ur1^4-350*ur1^6+10*e1^2*(50+84*ur1^2+105*ur1^4))))+a^4*r1^3*(156*l1^6*(2*M-r1)+r1*(-8784*M^6+24*M^5*r1*(13+170*ur1^2)+12*M^4*r1^2*(1459-64*ur1^2+281*ur1^4)+4*M^2*r1^4*(-4199+4942*ur1^2-2484*ur1^4+9*ur1^6)+2*M*r1^5*(9546-4777*ur1^2+298*ur1^4+516*ur1^6)-2*M^3*r1^3*(1955+8226*ur1^2-909*ur1^4+1140*ur1^6)+r1^6*(-9882+1951*ur1^2+1689*ur1^4+e1^2*(9906-5597*ur1^2)))+l1^2*(8992*M^5-16*M^4*r1*(638+1583*ur1^2)-8*M^2*r1^3*(-2835-5368*ur1^2+565*ur1^4)+8*M^3*r1^2*(-736+683*ur1^2+3764*ur1^4)-2*M*r1^4*(12622+15641*ur1^2+9648*ur1^4)+r1^5*(19832+8637*ur1^2+108*ur1^4-468*e1^2*(49+3*ur1^2)))-6*l1^4*(1824*M^3-8*M^2*r1*(414+361*ur1^2)+4*M*r1^2*(749+328*ur1^2+700*ur1^4)-r1^3*(803-202*ur1^2-350*ur1^4+2*e1^2*(93+105*ur1^2+175*ur1^4))))+r1^5*(12*l1^6*(2*M-r1)*(68*M^2-2*M*r1*(86+105*ur1^2)+5*r1^2*(34+63*ur1^2+70*ur1^4))+l1^2*r1^3*(9648*M^4+2*M*r1^3*(-28898-22971*ur1^2-2706*ur1^4+18*e1^2*(599+48*ur1^2))+72*M^3*r1*(62*e1^2-7*(44+51*ur1^2))+12*M^2*r1^2*(3199+3561*ur1^2+716*ur1^4-2*e1^2*(469+54*ur1^2))+r1^4*(21470+36153*ur1^2+1674*ur1^4-18*e1^2*(1621+92*ur1^2)))-r1^5*(4896*M^4+24*M^3*r1*(-557+117*e1^2+210*ur1^2)+36*M^2*r1^2*(564-235*ur1^2-76*ur1^4+3*e1^2*(-52+29*ur1^2))+2*M*r1^3*(-11407+3834*ur1^2+2040*ur1^4+36*ur1^6-9*e1^2*(-403+261*ur1^2))+r1^4*(7696+2695*ur1^2-4749*ur1^4-36*ur1^6+e1^2*(-7618+4959*ur1^2)))+6*l1^4*r1*(2240*M^4-8*M^3*r1*(658+36*e1^2+223*ur1^2)+4*M^2*r1^2*(2163+289*ur1^2+140*ur1^4+2*e1^2*(53+105*ur1^2))+r1^4*(4507-702*ur1^2-1330*ur1^4-700*ur1^6+10*e1^2*(34+63*ur1^2+70*ur1^4))-4*M*r1^3*(3076-217*ur1^2-385*ur1^4-175*ur1^6+e1^2*(104+210*ur1^2+175*ur1^4)))))*ΔQ^4*Δθ^2)/(6*r1^3*(a^2+r1*(-2*M+r1))^4)+((3*a^10*(58*M+3*r1+6*e1^2*r1)+6*a^9*e1*l1*(-34*M+3*(-1+e1^2)*r1)+6*a^7*e1*l1*r1*(-3*l1^2+106*M^2+4*M*r1*(-37+83*ur1^2)+3*r1^2*(-9-4*ur1^2+3*e1^2*(3+ur1^2)))+6*a^5*e1*l1*r1^2*(-20*M^3+2*M^2*r1*(177-731*ur1^2)+2*M*r1^2*(-201+614*ur1^2+225*ur1^4)-l1^2*(70*M+3*r1*(8+3*ur1^2))+3*r1^3*(-33-29*ur1^2-3*ur1^4+3*e1^2*(11+7*ur1^2)))+6*a^3*e1*l1*r1^3*(-112*M^4+4*M^3*r1*(-32+399*ur1^2)+2*M*r1^3*(-482+965*ur1^2+424*ur1^4)-2*M^2*r1^2*(-361+1752*ur1^2+450*ur1^4)+l1^2*(232*M^2-3*r1^2*(25+18*ur1^2)-20*M*r1*(31+36*ur1^2))+3*r1^4*(-65-79*ur1^2-18*ur1^4+e1^2*(65+54*ur1^2)))+a^8*(3*l1^2*(68*M+(5-2*e1^2)*r1)-r1*(948*M^2+M*r1*(-677+444*ur1^2)+r1^2*(131+3*ur1^2+3*e1^2*(-73+11*ur1^2))))-12*a*e1*l1*r1^4*(l1^2*(108*M^3+6*r1^3*(10+9*ur1^2)-4*M^2*r1*(127+108*ur1^2)+M*r1^2*(831+1188*ur1^2+350*ur1^4))+r1*(16*M^4+2*M^3*r1*(87+18*e1^2-503*ur1^2)-6*r1^4*(-1+e1^2-ur1^2)*(10+9*ur1^2)+M^2*r1^2*(-609+1263*ur1^2+386*ur1^4-6*e1^2*(10+9*ur1^2))+M*r1^3*(796-874*ur1^2-217*ur1^4+e1^2*(66+63*ur1^2))))+a^6*r1*(6*l1^4+l1^2*(-636*M^2+3*M*r1*(251-664*ur1^2)+r1^2*(-389-330*ur1^2+3*e1^2*(71+126*ur1^2)))+r1*(1524*M^3+6*M^2*r1*(-497+580*ur1^2)-6*M*r1^2*(-365+261*ur1^2+39*ur1^4)+r1^3*(-1043+117*ur1^2+51*ur1^4+3*e1^2*(373-110*ur1^2+3*ur1^4))))+a^2*r1^3*(-3*l1^4*(464*M^2-10*M*r1*(113+144*ur1^2)+r1^2*(449+729*ur1^2+350*ur1^4))+r1*(-720*M^5+8*M^4*r1*(-89+849*ur1^2)-4*M^3*r1^2*(-1669+2373*ur1^2+420*ur1^4)-2*M*r1^4*(-5350+1524*ur1^2+690*ur1^4+111*ur1^6)+2*M^2*r1^3*(-5445+3354*ur1^2+1061*ur1^4+240*ur1^6)+r1^5*(-5366+291*ur1^2+739*ur1^4-27*ur1^6+3*e1^2*(1757-836*ur1^2+36*ur1^4)))+l1^2*(672*M^4+12*M^3*r1*(191-798*ur1^2)+12*M^2*r1^2*(-702+763*ur1^2+450*ur1^4)+3*M*r1^3*(4179+1030*ur1^2+826*ur1^4)+r1^4*(-6663-6894*ur1^2-5324*ur1^4-1050*ur1^6+75*e1^2*(59+90*ur1^2+42*ur1^4))))+a^4*r1^2*(3*l1^4*(140*M-r1*(73+126*ur1^2))+r1*(-288*M^4-60*M^3*r1*(-59+143*ur1^2)+6*M^2*r1^2*(-1099+1316*ur1^2+218*ur1^4)-M*r1^3*(-6120+2784*ur1^2+977*ur1^4+240*ur1^6)+r1^4*(-3177+393*ur1^2+233*ur1^4-9*ur1^6+3*e1^2*(1045-429*ur1^2+18*ur1^4)))+3*l1^2*(40*M^3+2*M^2*r1*(-371+1462*ur1^2)+M*r1^2*(1371-1093*ur1^2-900*ur1^4)+r1^3*(-837-791*ur1^2-497*ur1^4+e1^2*(522+855*ur1^2+350*ur1^4))))+r1^4*(3*l1^4*(2*M-r1)*(216*M^2-8*M*r1*(89+108*ur1^2)+r1^2*(1026+1521*ur1^2+700*ur1^4))+r1^3*(-2376*M^4-4*M^3*r1*(-1579+342*e1^2+450*ur1^2)+M*r1^3*(9411-1626*ur1^2-1093*ur1^4+18*ur1^6-6*e1^2*(524-264*ur1^2+9*ur1^4))+r1^4*(-3092-1554*ur1^2+1349*ur1^4-45*ur1^6+3*e1^2*(1018-506*ur1^2+21*ur1^4))-6*M^2*r1^2*(22*e1^2*(-20+9*ur1^2)-3*(-501+138*ur1^2+49*ur1^4)))-l1^2*r1*(1608*M^4+4*M^3*r1*(-1525+174*e1^2+303*ur1^2)+6*M^2*r1^2*(2139+368*ur1^2+726*ur1^4-10*e1^2*(23+45*ur1^2))+M*r1^3*(-17349-9093*ur1^2-8926*ur1^4-2100*ur1^6+12*e1^2*(194+333*ur1^2+175*ur1^4))+r1^4*(6128+6015*ur1^2+6614*ur1^4+2100*ur1^6-3*e1^2*(1026+1521*ur1^2+700*ur1^4)))))*ΔQ^2*Δθ^4)/(12*(a^2+r1*(-2*M+r1))^4)+(r1^3*(a^8*(57-36*e1^2)+264*a^5*e1*l1*M*r1-12*a^3*e1*l1*M*r1^2*(16*M+r1*(-29+66*ur1^2))-12*a*e1*l1*M*r1^3*(8*M^2-10*M*r1*(5+8*ur1^2)+r1^2*(41+200*ur1^2+46*ur1^4))+a^6*(36*l1^2+r1*(-267*M+r1*(208-6*ur1^2+3*e1^2*(-53+26*ur1^2))))-3*a^4*r1*(l1^2*(88*M+r1*(-41+26*ur1^2))+r1*(-86*M^2+M*r1*(163-118*ur1^2)+r1^2*(-79+98*ur1^2+81*ur1^4+e1^2*(72-161*ur1^2-46*ur1^4))))+a^2*r1^2*(3*l1^2*(64*M^2+2*M*r1*(-47+132*ur1^2)+r1^2*(31-135*ur1^2-46*ur1^4))+r1*(348*M^3-12*M^2*r1*(29+110*ur1^2)+3*M*r1^2*(37+616*ur1^2+367*ur1^4)+r1^3*(-66-1017*ur1^2-880*ur1^4-132*ur1^6+9*e1^2*(5+126*ur1^2+46*ur1^4))))+r1^3*(3*l1^2*(2*M-r1)*(16*M^2-32*M*r1*(2+5*ur1^2)+r1^2*(46+243*ur1^2+92*ur1^4))+r1*(-504*M^4+4*M^3*r1*(247-78*e1^2+318*ur1^2)+6*M^2*r1^2*(-167-392*ur1^2-205*ur1^4+6*e1^2*(11+17*ur1^2))+M*r1^3*(621+2496*ur1^2+1733*ur1^4+264*ur1^6-12*e1^2*(24+67*ur1^2+23*ur1^4))+r1^4*(-152-873*ur1^2-1039*ur1^4-270*ur1^6+3*e1^2*(46+243*ur1^2+92*ur1^4)))))*Δθ^6)/(48*(a^2+r1*(-2*M+r1))^4))+Δr^2*((4*ur1*(2*a^13*e1*M*(98*M^3+57*M^2*r1-32*M*r1^2-18*r1^3)+a^12*l1*M*(-196*M^3+166*M^2*r1+307*M*r1^2+108*r1^3)-2*a^11*e1*M*r1*(488*M^4+l1^2*(229*M^2+328*M*r1+126*r1^2)+2*M*r1^3*(23-246*ur1^2)+10*r1^4*(13-9*ur1^2)-2*M^3*r1*(59+293*ur1^2)-M^2*r1^2*(578+917*ur1^2))-2*a^9*e1*M*r1^2*(-584*M^5+4*l1^4*(103*M+65*r1)+4*r1^5*(97-114*ur1^2)+6*M^3*r1^2*(257+147*ur1^2)+4*M^4*r1*(287+293*ur1^2)-2*M*r1^4*(213+835*ur1^2)-M^2*r1^3*(1500+1397*ur1^2)+l1^2*(164*M^3+M^2*r1*(181-2562*ur1^2)+6*M*r1^2*(139-456*ur1^2)+4*r1^3*(173-180*ur1^2)))+6*a*e1*M*r1^6*(12*l1^8*(2*M-5*r1)+28*l1^6*(2*M-r1)*r1*(8*M-r1*ur1^2)-l1^2*(2*M-r1)*r1^5*(214*M+3*r1*(-39+46*ur1^2))-(2*M-r1)*r1^7*(70*M+r1*(-32+61*ur1^2))+l1^4*r1^3*(128*M^2+M*r1*(94-280*ur1^2)+r1^2*(-157+140*ur1^2)))+2*a^3*e1*M*r1^5*(24*l1^8+42*l1^6*(12*M^2-4*M*r1*(3+5*ur1^2)+r1^2*(-5+12*ur1^2))+2*l1^4*r1*(1212*M^3+M*r1^2*(331-1050*ur1^2)+5*r1^3*(-103+189*ur1^2)-2*M^2*r1*(29+420*ur1^2))+r1^5*(288*M^3+2*M*r1^2*(645-278*ur1^2)-8*M^2*r1*(139+108*ur1^2)+r1^3*(-394+677*ur1^2))+l1^2*r1^3*(2352*M^3+2*M*r1^2*(1651-816*ur1^2)-8*M^2*r1*(353+441*ur1^2)+3*r1^3*(-423+704*ur1^2)))+a^10*l1*r1*(l1^2*(458*M^3+1015*M^2*r1+458*M*r1^2+(-1+e1^2)*r1^3)+M*(976*M^4+3*M*r1^3*(123-103*ur1^2)+6*r1^4*(103+4*ur1^2)-2*M^3*r1*(989+586*ur1^2)-M^2*r1^2*(1831+1104*ur1^2)))-2*a^7*e1*M*r1^3*(210*l1^6-2*l1^4*(86*M^2+6*M*r1*(-47+175*ur1^2)+r1^2*(-491+525*ur1^2))+r1*(-1176*M^5+r1^5*(660-953*ur1^2)+12*M^4*r1*(-78+61*ur1^2)-4*M*r1^4*(337+452*ur1^2)+M^2*r1^3*(-646+937*ur1^2)+2*M^3*r1^2*(2035+1281*ur1^2))+l1^2*(-1244*M^4+r1^4*(1573-2664*ur1^2)+84*M^3*r1*(2+61*ur1^2)+M^2*r1^2*(95+1848*ur1^2)-2*M*r1^3*(161+2838*ur1^2)))+a^8*l1*r1^2*(-1168*M^6+6*r1^6+l1^4*(824*M^2+712*M*r1-r1^2)+2*M^4*r1^2*(1244-1549*ur1^2)+8*M^5*r1*(716+293*ur1^2)+3*M*r1^5*(469+22*ur1^2+240*ur1^4)+M^3*r1^3*(-4903-5399*ur1^2+2646*ur1^4)+M^2*r1^4*(-2855-2592*ur1^2+2772*ur1^4)+l1^2*(328*M^4+2*M^2*r1^2*(142-2309*ur1^2)+2*M*r1^3*(910-437*ur1^2)+r1^4*(-13+13*e1^2-ur1^2)-M^3*r1*(2515+5124*ur1^2)))+2*a^5*e1*M*r1^4*(84*l1^6*(2*M+5*r1*(-1+ur1^2))+l1^4*(1304*M^3+20*M*r1^2*(11+42*ur1^2)-40*M^2*r1*(13+105*ur1^2)+3*r1^3*(-481+840*ur1^2))+r1^3*(2844*M^4-18*M^3*r1*(102+35*ur1^2)+4*M*r1^3*(449+110*ur1^2)+r1^4*(-682+1081*ur1^2)-M^2*r1^2*(1025+2049*ur1^2))+l1^2*r1*(1524*M^4-4*M^3*r1*(-311+531*ur1^2)+2*M*r1^3*(1393+1128*ur1^2)+r1^4*(-1925+3642*ur1^2)-M^2*r1^2*(2075+7698*ur1^2)))-3*l1*r1^6*(12*l1^8*(4*M^2-8*M*r1+3*r1^2)+4*l1^6*r1*(116*M^3+9*r1^3*(1-e1^2+ur1^2)+M*r1^2*(5+17*e1^2+30*ur1^2)-2*M^2*r1*(52+11*e1^2+36*ur1^2))+l1^4*(2*M-r1)*r1^3*(340*M^2-51*r1^2-7*M*r1*(21+68*ur1^2))+l1^2*r1^5*(188*M^3+r1^3*(58-57*e1^2+60*ur1^2)+3*M*r1^2*(-35+18*e1^2+102*ur1^2)-4*M^2*r1*(29+9*e1^2+174*ur1^2))+(2*M-r1)*r1^7*(10*M^2-M*r1*(4+81*ur1^2)+r1^2*(-1-ur1^2+6*ur1^4)))-a^2*l1*r1^5*(24*l1^8*(2*M-r1)+12*l1^6*(84*M^3+r1^3*(7-7*e1^2-2*ur1^2)-14*M^2*r1*(7+10*ur1^2)+M*r1^2*(26+111*ur1^2))+l1^4*r1*(3480*M^4+139*r1^4-12*M^3*r1*(159+616*ur1^2)+M*r1^3*(463+4536*ur1^2-1260*ur1^4)+24*M^2*r1^2*(-58-105*ur1^2+105*ur1^4))+3*r1^5*(2344*M^4-4*M^3*r1*(643+650*ur1^2)+M*r1^3*(-43+235*ur1^2-258*ur1^4)+r1^4*(1-7*ur1^2-6*ur1^4)+4*M^2*r1^2*(196+256*ur1^2+129*ur1^4))+l1^2*r1^3*(8520*M^4+r1^4*(328-307*e1^2+163*ur1^2)-12*M^3*r1*(757+1124*ur1^2)+M*r1^3*(-467+3813*ur1^2-2100*ur1^4)+6*M^2*r1^2*(419+165*ur1^2+700*ur1^4)))-a^6*l1*r1^3*(-30*l1^6*(14*M+r1-e1^2*r1)+2*l1^4*(172*M^3+6*r1^3+M*r1^2*(-857+840*ur1^2)+2*M^2*r1*(193+1050*ur1^2))+l1^2*(2488*M^5+3*r1^5*(28-23*e1^2+4*ur1^2)-8*M^4*r1*(674+1281*ur1^2)+2*M^3*r1^2*(8+1421*ur1^2)+M^2*r1^3*(6039+13754*ur1^2-4200*ur1^4)+M*r1^4*(-2541+3518*ur1^2-2100*ur1^4))+r1*(4488*M^6+4*M^5*r1*(25-2067*ur1^2)-3*r1^6*(5+9*ur1^2)+M^2*r1^4*(8157+7193*ur1^2-4374*ur1^4)-3*M*r1^5*(511-17*ur1^2+756*ur1^4)+2*M^4*r1^2*(-5353-2846*ur1^2+2646*ur1^4)+M^3*r1^3*(-2599+4046*ur1^2+2898*ur1^4)))+a^4*l1*r1^4*(30*l1^8-6*l1^6*(56*M^2+r1^2*(-9+9*e1^2-5*ur1^2)+2*M*r1*(-31+70*ur1^2))-2*l1^4*(1304*M^4+39*r1^4-14*M^3*r1*(121+300*ur1^2)+2*M^2*r1^2*(563+1134*ur1^2)-14*M*r1^3*(29-171*ur1^2+45*ur1^4))+r1^3*(-7212*M^5+3*r1^5*(3+17*ur1^2)+2*M^4*r1*(466+3603*ur1^2)+M^3*r1^2*(13353+6145*ur1^2-6084*ur1^4)-2*M^2*r1^3*(3823+4294*ur1^2+27*ur1^4)+3*M*r1^4*(257-187*ur1^2+774*ur1^4))+l1^2*r1*(-4524*M^5+r1^5*(-226+193*e1^2-75*ur1^2)+4*M^4*r1*(-83+3477*ur1^2)-2*M^2*r1^3*(4115+6168*ur1^2)+M^3*r1^2*(12565+14814*ur1^2-8400*ur1^4)+M*r1^4*(1493-5503*ur1^2+4200*ur1^4))))*ΔQ^6*ΔR)/(3*r1^7*(a^2+r1*(-2*M+r1))^3)+(ur1*(4*a^11*e1*M*(317*M^2+162*M*r1-6*r1^2)-a^10*l1*(1268*M^3+626*M^2*r1+2*M*r1^2+31*(-1+e1^2)*r1^3)+4*a^9*e1*M*r1*(-1460*M^3+l1^2*(160*M+19*r1)+6*r1^3*(-23+57*ur1^2)+2*M*r1^2*(379+629*ur1^2)+M^2*r1*(625+1177*ur1^2))-a^8*l1*r1*(-5840*M^4+l1^2*(640*M^2+160*M*r1+(-91+60*e1^2)*r1^2)+r1^4*(-367+403*e1^2-31*ur1^2)+2*M*r1^3*(307+889*ur1^2)+2*M^3*r1*(1295+2354*ur1^2)+2*M^2*r1^2*(1988+3315*ur1^2))+12*a*e1*M*r1^5*(84*l1^6*(2*M-5*r1*(1+ur1^2))-3*(2*M-r1)*r1^5*(70*M+r1*(-34+61*ur1^2))+4*l1^2*r1^3*(161*M^2-6*M*r1*(45+46*ur1^2)+r1^2*(397+138*ur1^2))+4*l1^4*r1*(378*M^2-21*M*r1*(17+20*ur1^2)+r1^2*(239+210*ur1^2)))+4*a^7*e1*M*r1^2*(54*l1^4+1652*M^4+8*M*r1^3*(199+334*ur1^2)+4*r1^4*(-161+341*ur1^2)-M^2*r1^2*(1005+808*ur1^2)-2*M^3*r1*(1972+1177*ur1^2)+l1^2*(-2116*M^2+6*r1^2*(41+396*ur1^2)+4*M*r1*(31+1191*ur1^2)))-8*a^3*e1*M*r1^4*(126*l1^6-3*l1^4*(440*M^2-14*M*r1*(58+75*ur1^2)+5*r1^2*(71+189*ur1^2))+r1^3*(-504*M^3+r1^3*(499-860*ur1^2)+4*M^2*r1*(281+243*ur1^2)+M*r1^2*(-1443+685*ur1^2))+l1^2*r1*(-2652*M^3+2*M*r1^2*(808+1173*ur1^2)+2*M^2*r1*(217+1710*ur1^2)-r1^3*(1625+2856*ur1^2)))-4*a^5*e1*M*r1^3*(42*l1^4*(34*M-3*r1*(6+25*ur1^2))-2*l1^2*(1796*M^3+12*r1^3*(51+268*ur1^2)-6*M^2*r1*(371+794*ur1^2)+M*r1^2*(-641+1716*ur1^2))+r1*(-3708*M^4+43*r1^4*(28-51*ur1^2)-6*M*r1^3*(440+171*ur1^2)+2*M^3*r1*(458+531*ur1^2)+M^2*r1^2*(2461+3665*ur1^2)))+a^6*l1*r1^2*(-6608*M^5+l1^4*(-216*M+60*r1)+3*r1^5*(663-713*e1^2+160*ur1^2)+8*M^4*r1*(1868+1177*ur1^2)+2*M^3*r1^2*(3688+3517*ur1^2)+2*M*r1^4*(-1959-3071*ur1^2+828*ur1^4)+2*M^2*r1^3*(-3525-7397*ur1^2+1710*ur1^4)+2*l1^2*(4232*M^3+6*r1^3*(72-50*e1^2+5*ur1^2)-4*M^2*r1*(121+2382*ur1^2)-M*r1^2*(2069+6000*ur1^2)))+a^4*l1*r1^3*(l1^2*(-14368*M^4+9*r1^4*(431-260*e1^2+52*ur1^2)-8*M^2*r1^2*(-1541+75*ur1^2)+16*M^3*r1*(917+2382*ur1^2)-2*M*r1^3*(7591+15456*ur1^2))+r1*(-12984*M^5+4*M^4*r1*(2+759*ur1^2)+r1^5*(5641-5983*e1^2+1851*ur1^2)+2*M^3*r1^2*(9597+10961*ur1^2-3420*ur1^4)+4*M^2*r1^3*(212-2888*ur1^2+27*ur1^4)+2*M*r1^4*(-5755-5440*ur1^2+1548*ur1^4))+12*l1^4*(476*M^2-2*M*r1*(139+525*ur1^2)+3*r1^2*(-1-35*ur1^2+7*e1^2*(2+5*ur1^2))))-3*l1*r1^5*(168*l1^6*(2*M-r1)*(2*M-r1*(3+5*ur1^2))+l1^2*r1^3*(5624*M^3+r1^3*(-2613+920*e1^2-922*ur1^2)+12*M^2*r1*(-731+60*e1^2-396*ur1^2)+2*M*r1^2*(4103-480*e1^2+1490*ur1^2))+r1^5*(2352*M^3+4*M^2*r1*(-1097+279*e1^2-522*ur1^2)+r1^3*(-1717+1767*e1^2-1757*ur1^2-36*ur1^4)+2*M*r1^2*(2520-837*e1^2+1070*ur1^2+36*ur1^4))-24*l1^4*r1*(-134*M^3+M^2*r1*(151+28*e1^2+98*ur1^2)+r1^3*(16-56*ur1^2-35*ur1^4+7*e1^2*(3+5*ur1^2))+M*r1^2*(-74+35*ur1^2+35*ur1^4-7*e1^2*(4+5*ur1^2))))+a^2*l1*r1^4*(252*l1^6*(4*M-r1*(2+5*ur1^2))-2*l1^2*r1*(6192*M^4+r1^4*(-4217+2280*e1^2-867*ur1^2)-36*M^3*r1*(-67+154*ur1^2)-18*M^2*r1^2*(903+890*ur1^2)+M*r1^3*(13333+13308*ur1^2))+r1^3*(-12720*M^4+24*M^3*r1*(244+703*ur1^2)+12*M^2*r1^2*(1233+254*ur1^2-240*ur1^4)+r1^4*(9139-9517*e1^2+4162*ur1^2+108*ur1^4)+2*M*r1^3*(-9151-5529*ur1^2+720*ur1^4))-12*l1^4*(880*M^3+42*M*r1^2*(13+27*ur1^2)-2*M^2*r1*(661+1050*ur1^2)+r1^3*(32+357*ur1^2+105*ur1^4-21*e1^2*(8+15*ur1^2)))))*ΔQ^4*ΔR*Δθ^2)/(6*r1^4*(a^2+r1*(-2*M+r1))^3)-(ur1*(-2*a^9*e1*M*(272*M+63*r1)+a^8*l1*(544*M^2+660*M*r1+3*(-25+28*e1^2)*r1^2)+a^6*l1*r1*(-2224*M^3+3*l1^2*(410*M+(31-56*e1^2)*r1)+4*M^2*r1*(-549+422*ur1^2)+M*r1^2*(2839+1944*ur1^2)-r1^3*(745+84*ur1^2+3*e1^2*(-250+9*ur1^2)))-2*a^7*e1*r1*(3*l1^2*(205*M+9*(-1+e1^2)*r1)+M*(-1112*M^2+4*M*r1*(148+211*ur1^2)+r1^2*(46+435*ur1^2)))-6*a*e1*r1^4*(-3*M*(2*M-r1)*r1^3*(70*M+r1*(-31+61*ur1^2))+4*l1^4*(116*M^2-27*r1^2-M*r1*(344+175*ur1^2))+l1^2*r1*(1852*M^3+12*M^2*r1*(-208+9*e1^2-115*ur1^2)+108*r1^3*(-1+e1^2-ur1^2)+M*r1^2*(2257-126*e1^2+690*ur1^2)))-2*a^5*e1*r1^2*(-27*l1^4-3*l1^2*(1016*M^2+9*r1^2*(7-7*e1^2+ur1^2)-M*r1*(971+786*ur1^2))+M*(1136*M^3+2*M*r1^2*(494+311*ur1^2)-4*M^2*r1*(509+422*ur1^2)+r1^3*(-384+1295*ur1^2)))+2*a^3*e1*r1^3*(6*l1^4*(190*M+27*r1)+M*r1*(-1152*M^3+r1^3*(646-1409*ur1^2)+16*M*r1^2*(-117+67*ur1^2)+8*M^2*r1*(199+162*ur1^2))+l1^2*(-3636*M^3+162*r1^3*(3-3*e1^2+ur1^2)+36*M^2*r1*(243+131*ur1^2)-3*M*r1^2*(1973+1476*ur1^2)))+l1*r1^4*(3*l1^4*(2*M-r1)*(464*M-5*r1*(183+140*ur1^2))+r1^3*(4068*M^3+2*M^2*r1*(-3614+972*e1^2-1539*ur1^2)+M*r1^2*(7933+2949*ur1^2-54*ur1^4+18*e1^2*(-154+9*ur1^2))+r1^3*(-2668-2589*ur1^2+135*ur1^4-3*e1^2*(-928+63*ur1^2)))-l1^2*r1*(-4980*M^3+4*M^2*r1*(1420+303*e1^2-57*ur1^2)+M*r1^2*(-1597+5878*ur1^2+2100*ur1^4-84*e1^2*(24+25*ur1^2))+r1^3*(1-4922*ur1^2-2100*ur1^4+15*e1^2*(183+140*ur1^2))))+a^4*l1*r1^2*(168*l1^4+2272*M^4-4*M^3*r1*(-771+844*ur1^2)-4*M^2*r1^2*(2129+934*ur1^2)+3*M*r1^3*(2213+1823*ur1^2+240*ur1^4)-3*r1^4*(849+158*ur1^2-9*ur1^4+18*e1^2*(-49+3*ur1^2))+l1^2*(-6096*M^2+9*M*r1*(437+524*ur1^2)+r1^2*(611+1263*ur1^2-3*e1^2*(439+350*ur1^2))))+a^2*l1*r1^3*(-3*l1^4*(760*M-r1*(383+350*ur1^2))+r1*(-2760*M^4+32*M^3*r1*(233+96*ur1^2)+9*M*r1^3*(1069+612*ur1^2+74*ur1^4)-2*M^2*r1^2*(5806+4125*ur1^2+720*ur1^4)-3*r1^4*(1515+531*ur1^2-27*ur1^4+4*e1^2*(-397+27*ur1^2)))+l1^2*(7272*M^3-24*M^2*r1*(482+393*ur1^2)+2*M*r1^2*(2138+1011*ur1^2)+r1^3*(1903+4340*ur1^2+1050*ur1^4-6*e1^2*(649+525*ur1^2)))))*ΔQ^2*ΔR*Δθ^4)/(12*r1*(a^2+r1*(-2*M+r1))^3)+(r1*ur1*(6*a^7*e1*M*(12*e1^2*M+17*r1)-3*a^6*l1*((34*M-15*r1)*r1+4*e1^2*M*(18*M+11*r1))+l1*r1^5*(1308*M^3+2*M^2*r1*(-748+342*e1^2-927*ur1^2)+2*r1^3*(-22+3*ur1^2+9*ur1^4)+M*r1^2*(509+933*ur1^2+792*ur1^4-36*e1^2*(10+23*ur1^2)))+6*a^5*e1*M*(4*l1^2*(9*M+11*r1)+r1^2*(72*(-1+e1^2)*M+r1*(5+6*e1^2+61*ur1^2)))-6*a^3*e1*M*r1^2*(-2*l1^2*(10*M+3*r1*(19+46*ur1^2))-r1*((76-24*e1^2)*M^2+2*M*r1*(16+42*e1^2-67*ur1^2)+r1^2*(-41+12*e1^2+116*ur1^2)))+6*a*e1*M*r1^3*(r1^2*(-92*M^2+2*M*r1*(52+12*e1^2-73*ur1^2)+r1^2*(-29+6*e1^2+55*ur1^2))+l1^2*(-24*M^2-116*M*r1+2*r1^2*(35+138*ur1^2)))-a^4*l1*(12*l1^2*M*(6*M+11*r1)+r1^2*(12*(-36+59*e1^2)*M^2+r1^2*(-46+81*ur1^2)+3*M*r1*(13+122*ur1^2+4*e1^2*(52+69*ur1^2))))+a^2*l1*r1^2*(12*l1^2*M*(13*M-r1*(8+69*ur1^2))+r1*(24*(-19+12*e1^2)*M^3+12*M^2*r1*(-61+16*e1^2+67*ur1^2)+r1^3*(-43-75*ur1^2+18*ur1^4)+M*r1^2*(572+777*ur1^2-12*e1^2*(71+138*ur1^2)))))*ΔR*Δθ^6)/(48*(a^2+r1*(-2*M+r1))^3))+Δr*((16*(-2*a^13*e1*l1*M^2*(50*M^2+49*M*r1+12*r1^2)+a^14*M^2*(62*M^2+67*M*r1+18*r1^2)-2*a^11*e1*l1*M*r1*(40*M^4+l1^2*M*(65*M+24*r1)+M^2*r1^2*(302-1015*ur1^2)+M^3*r1*(342-686*ur1^2)+2*M*r1^3*(23-258*ur1^2)-6*r1^4*(2+15*ur1^2))-2*a^9*e1*l1*M*r1^2*(-280*M^5+4*l1^4*(5*M-r1)+M^2*r1^3*(844-1471*ur1^2)-2*r1^5*(32+213*ur1^2)+4*M^4*r1*(-151+343*ur1^2)+2*M^3*r1^2*(233+459*ur1^2)-2*M*r1^4*(-63+815*ur1^2)+l1^2*(220*M^3+M^2*r1*(565-910*ur1^2)+2*M*r1^2*(37-468*ur1^2)-6*r1^3*(7+40*ur1^2)))+6*a*e1*l1*M*r1^6*(4*l1^8*(2*M-5*r1)+2*l1^6*(2*M-r1)*r1*(32*M+r1*(-7+6*ur1^2))+l1^4*r1^3*(280*M^2+r1^2*(237-14*ur1^2)+2*M*r1*(-151+14*ur1^2))+l1^2*(2*M-r1)*r1^5*(38*M-r1*(7+18*ur1^2))+(2*M-r1)*r1^7*(18*M-r1*(8+53*ur1^2)))+a^12*M*(l1^2*M*(100*M^2+181*M*r1+60*r1^2)-r1*(92*M^4+30*r1^4*ur1^2+8*M^3*r1*(-39+8*ur1^2)+4*M^2*r1^2*(-127+41*ur1^2)+M*r1^3*(-167+126*ur1^2)))-2*a^3*e1*l1*M*r1^5*(12*l1^8-12*l1^6*(18*M^2+r1^2*(7+2*ur1^2)-2*M*r1*(16+5*ur1^2))-2*l1^4*r1*(444*M^3-15*M*r1^2*(47+14*ur1^2)+2*M^2*r1*(131+42*ur1^2)+r1^3*(340+63*ur1^2))+l1^2*r1^3*(-1704*M^3+4*M^2*r1*(77+90*ur1^2)+2*M*r1^2*(291+268*ur1^2)-r1^3*(119+412*ur1^2))+r1^5*(-504*M^3+4*M^2*r1*(7+162*ur1^2)+2*M*r1^2*(159+250*ur1^2)-r1^3*(100+571*ur1^2)))-2*a^7*e1*l1*M*r1^3*(2*l1^4*(134*M^2+M*r1*(88-210*ur1^2)-3*r1^2*(18+35*ur1^2))+l1^2*(-700*M^4+2*M*r1^3*(145-782*ur1^2)+52*M^3*r1*(-8+35*ur1^2)-r1^4*(161+780*ur1^2)+M^2*r1^2*(1647+872*ur1^2))+r1*(-72*M^5+12*M^4*r1*(-102+71*ur1^2)-4*M*r1^4*(-69+400*ur1^2)-r1^5*(144+835*ur1^2)+M^2*r1^3*(1126+875*ur1^2)+2*M^3*r1^2*(-167+1275*ur1^2)))-2*a^5*e1*l1*M*r1^4*(6*l1^6*(18*M-r1*(7+10*ur1^2))+l1^4*(-616*M^3+4*M*r1^2*(208+21*ur1^2)+24*M^2*r1*(19+35*ur1^2)-r1^3*(397+378*ur1^2))+r1^3*(-612*M^4+16*M*r1^3*(25-19*ur1^2)+6*M^3*r1*(-158+75*ur1^2)-r1^4*(168+911*ur1^2)+M^2*r1^2*(671+1731*ur1^2))+l1^2*r1*(-660*M^4+2*M*r1^3*(333-104*ur1^2)+4*M^3*r1*(-517+45*ur1^2)-r1^4*(217+898*ur1^2)+M^2*r1^2*(1739+2126*ur1^2)))-3*r1^6*(4*l1^10*(4*M^2-8*M*r1+3*r1^2)+4*l1^8*r1*(28*M^3+3*r1^3*(1-e1^2+ur1^2)+M*r1^2*(-1+4*e1^2+7*ur1^2)-2*M^2*r1*(12+2*e1^2+9*ur1^2))+2*l1^6*(2*M-r1)*r1^3*(90*M^2+56*r1^2-M*r1*(79+77*ur1^2))+l1^4*r1^5*(304*M^3+4*M^2*r1*(-111+18*e1^2-118*ur1^2)+r1^3*(-113+114*e1^2-111*ur1^2)+2*M*r1^2*(186-54*e1^2+151*ur1^2))+(2*M-r1)*r1^9*(4*M^2-r1^2*ur1^2*(1+3*ur1^2)-2*M*(r1+6*r1*ur1^2))+l1^2*(2*M-r1)*r1^7*(32*M^2-6*M*r1*(3+20*ur1^2)+r1^2*(1+5*ur1^2+6*ur1^4)))+a^10*r1*(2*l1^4*(65*M^3+37*M^2*r1-2*M*r1^2-(-1+e1^2)*r1^3)+l1^2*M*(80*M^4+M*r1^3*(305-1212*ur1^2)-6*r1^4*(7+40*ur1^2)-14*M^3*r1*(-41+98*ur1^2)-9*M^2*r1^2*(-123+235*ur1^2))-M*r1*(376*M^5+4*M^4*r1*(373+58*ur1^2)+2*M^3*r1^2*(356-297*ur1^4)+6*r1^5*(1+27*ur1^2-15*ur1^4)-2*M*r1^4*(273-191*ur1^2+252*ur1^4)-3*M^2*r1^3*(330-26*ur1^2+315*ur1^4)))-a^2*r1^5*(12*l1^10*(-2*M+r1)+12*l1^8*(36*M^3+r1^3*(4-4*e1^2+ur1^2)-2*M^2*r1*(23+10*ur1^2)+M*r1^2*(10+19*ur1^2))+2*l1^6*r1*(168*M^4-133*r1^4-12*M^3*r1*(-57+91*ur1^2)+2*M*r1^3*(349+336*ur1^2-105*ur1^4)+12*M^2*r1^2*(-104-28*ur1^2+35*ur1^4))+3*r1^7*(-104*M^4+3*r1^4*ur1^2*(1+2*ur1^2)+16*M^3*r1*(8+3*ur1^2)+M*r1^3*(10+61*ur1^2-51*ur1^4)+2*M^2*r1^2*(-29-65*ur1^2+45*ur1^4))-3*l1^2*r1^5*(-168*M^4+20*M^3*r1*(-1+65*ur1^2)+2*M^2*r1^2*(105+64*ur1^2-258*ur1^4)+r1^4*(3+10*ur1^2+6*ur1^4)+M*r1^3*(-85-519*ur1^2+258*ur1^4))+l1^4*r1^3*(1008*M^4+12*M^3*r1*(63-440*ur1^2)+r1^4*(-608+614*e1^2-263*ur1^2)+M*r1^3*(1717+2601*ur1^2-1050*ur1^4)+6*M^2*r1^2*(-428-143*ur1^2+350*ur1^4)))+a^8*r1^2*(2*l1^6*(20*M^2-4*M*r1+r1^2)+2*l1^4*(220*M^4+M^2*r1^2*(131-959*ur1^2)+M^3*r1*(561-910*ur1^2)+r1^4*(13-13*e1^2+ur1^2)-M*r1^3*(98+257*ur1^2))-l1^2*M*(560*M^5+4*M^3*r1^2*(352+97*ur1^2)-4*M^4*r1*(-561+686*ur1^2)+M^2*r1^3*(-2085+4990*ur1^2-2646*ur1^4)+3*r1^5*(73+394*ur1^2-240*ur1^4)-3*M*r1^4*(229-1501*ur1^2+924*ur1^4))+M*r1*(624*M^6+240*M^5*r1*(5+3*ur1^2)+3*r1^6*(-10-127*ur1^2+132*ur1^4)-4*M^4*r1^2*(265-42*ur1^2+297*ur1^4)-4*M^3*r1^3*(681+127*ur1^2+324*ur1^4)+2*M^2*r1^4*(200+203*ur1^2+486*ur1^4)+M*r1^5*(918-302*ur1^2+1449*ur1^4)))+a^4*r1^4*(12*l1^8*(18*M^2+(-1+e1^2)*r1^2-M*r1*(7+10*ur1^2))-2*l1^6*(616*M^4-57*r1^4+2*M^2*r1^2*(-400+273*ur1^2)-84*M^3*(r1+10*r1*ur1^2)+M*r1^3*(470+651*ur1^2-210*ur1^4))-3*r1^5*(-384*M^5+3*r1^5*ur1^2*(1+ur1^2)+4*M^4*r1*(19+15*ur1^2)+M*r1^4*(20+141*ur1^2-168*ur1^4)+3*M^2*r1^3*(-59-68*ur1^2+7*ur1^4)+10*M^3*r1^2*(34-3*ur1^2+45*ur1^4))+l1^2*r1^3*(1800*M^5+3*r1^5*(3+5*ur1^2)+4*M^4*r1*(-605+1569*ur1^2)+2*M^3*r1^2*(261+2830*ur1^2-3042*ur1^4)+M^2*r1^3*(941-3271*ur1^2-54*ur1^4)+3*M*r1^4*(-155-902*ur1^2+774*ur1^4))+l1^4*r1*(984*M^5+2*M^2*r1^3*(1119-1970*ur1^2)+r1^5*(383-386*e1^2+114*ur1^2)+4*M^4*r1*(-868+1557*ur1^2)+2*M^3*r1^2*(567+2935*ur1^2-2100*ur1^4)+M*r1^4*(-1558-3385*ur1^2+2100*ur1^4)))+a^6*r1^3*(l1^6*(536*M^3+24*r1^3+28*M^2*r1*(13-30*ur1^2)-2*M*r1^2*(139+210*ur1^2))+r1^3*(1176*M^6-3*r1^6*ur1^2+36*M^5*r1*(37+32*ur1^2)+M^3*r1^3*(-809+530*ur1^2-1215*ur1^4)+3*M*r1^5*(-20-173*ur1^2+225*ur1^4)+2*M^2*r1^4*(451+124*ur1^2+594*ur1^4)-2*M^4*r1^2*(1151+228*ur1^2+1035*ur1^4))+l1^4*(-1400*M^5+2*M^3*r1^2*(1135-549*ur1^2)+6*r1^5*(23-23*e1^2+4*ur1^2)+56*M^4*r1*(-37+65*ur1^2)+2*M^2*r1^3*(493-2691*ur1^2+1050*ur1^4)+M*r1^4*(-825-2114*ur1^2+1050*ur1^4))+l1^2*r1*(1704*M^6+3*r1^6+4*M^5*r1*(-137+1623*ur1^2)+M^3*r1^3*(1573-895*ur1^2-2898*ur1^4)+3*M*r1^5*(-149-827*ur1^2+756*ur1^4)-2*M^4*r1^2*(2055-3676*ur1^2+2646*ur1^4)+M^2*r1^4*(957-6286*ur1^2+4374*ur1^4))))*ΔQ^8)/(3*r1^9*(a^2+r1*(-2*M+r1))^2)+(4*(13*a^12*M^2*(5*M+3*r1)-2*a^11*e1*l1*M^2*(5*M+6*r1)+2*a^9*e1*l1*M*r1*(-460*M^3+2*l1^2*(19*M+r1)+36*r1^3*(1+13*ur1^2)+2*M*r1^2*(-1+889*ur1^2)+M^2*r1*(-289+1715*ur1^2))+a^10*(l1^2*(10*M^3+7*M^2*r1-2*M*r1^2-(-1+e1^2)*r1^3)+M*r1*(178*M^3+M*r1^2*(427-528*ur1^2)+M^2*r1*(685-412*ur1^2)+6*r1^3*(1-28*ur1^2)))-4*a^3*e1*l1*M*r1^4*(21*l1^6-6*l1^4*(56*M^2-42*M*r1*(3+5*ur1^2)+r1^2*(67+189*ur1^2))-2*l1^2*r1*(714*M^3-2*M^2*r1*(82+405*ur1^2)-M*r1^2*(237+689*ur1^2)+r1^3*(79+781*ur1^2))+r1^3*(-648*M^3+4*M^2*r1*(-5+288*ur1^2)+M*r1^2*(411+803*ur1^2)-r1^3*(103+991*ur1^2)))+2*a^7*e1*l1*M*r1^2*(24*l1^4+940*M^4-10*M^3*r1*(76+343*ur1^2)+2*r1^4*(73+887*ur1^2)+4*M*r1^3*(-65+904*ur1^2)-M^2*r1^2*(1347+1112*ur1^2)+l1^2*(-800*M^2+12*r1^2*(8+109*ur1^2)+2*M*r1*(61+1294*ur1^2)))+2*a^5*e1*l1*M*r1^3*(-6*l1^4*(64*M-7*r1*(7+30*ur1^2))+l1^2*(1448*M^3-8*M^2*r1*(291+647*ur1^2)+2*M*r1^2*(-241+796*ur1^2)+r1^3*(245+3496*ur1^2))+r1*(1764*M^4+18*M*r1^3*(-42+73*ur1^2)+5*r1^4*(50+537*ur1^2)-2*M^3*r1*(-602+729*ur1^2)-M^2*r1^2*(1307+4819*ur1^2)))+6*a*e1*l1*M*r1^5*(2*l1^4*r1*(228*M^2-4*M*r1*(59+84*ur1^2)+r1^2*(185+168*ur1^2))+(2*M-r1)*r1^5*(66*M-r1*(22+201*ur1^2))+l1^2*r1^3*(200*M^2-6*M*r1*(27+104*ur1^2)+r1^2*(109+312*ur1^2))+14*l1^6*(2*M-5*(r1+2*r1*ur1^2)))+a^8*r1*(-(l1^4*(76*M^2+28*M*r1+(-13+12*e1^2)*r1^2))+l1^2*(920*M^4+9*M^2*r1^2*(11-549*ur1^2)+10*M^3*r1*(109-343*ur1^2)+r1^4*(13-13*e1^2+ur1^2)-2*M*r1^3*(58+805*ur1^2))+r1*(-1492*M^5-6*r1^5+8*M^4*r1*(-259+121*ur1^2)+24*M*r1^4*(-1-32*ur1^2+9*ur1^4)+M^3*r1^2*(439+956*ur1^2+747*ur1^4)+M^2*r1^3*(1217-1016*ur1^2+801*ur1^4)))+a^6*r1^2*(12*l1^6*(-4*M+r1)+2*l1^4*(800*M^3+6*r1^3*(11-10*e1^2+ur1^2)-4*M^2*r1*(-4+647*ur1^2)-M*r1^2*(269+1782*ur1^2))+l1^2*(-1880*M^5+3*r1^5*(14-23*e1^2+4*ur1^2)+74*M^3*r1^2*(31+73*ur1^2)+28*M^4*r1*(-51+245*ur1^2)+5*M^2*r1^3*(65-1844*ur1^2+342*ur1^4)+M*r1^4*(-639-5860*ur1^2+828*ur1^4))+r1*(1752*M^6+3*r1^6*(-8+3*ur1^2)-12*M^5*r1*(-91+24*ur1^2)+M^3*r1^3*(-1669+2860*ur1^2-855*ur1^4)+3*M*r1^5*(-36-463*ur1^2+246*ur1^4)-2*M^4*r1^2*(1513+240*ur1^2+747*ur1^4)+M^2*r1^4*(1747+538*ur1^2+1323*ur1^4)))+a^4*r1^3*(-4*l1^4*(724*M^4+3*r1^4*(-40+39*e1^2-9*ur1^2)-M^2*r1^2*(449+5*ur1^2)-4*M^3*r1*(159+647*ur1^2)+M*r1^3*(482+2325*ur1^2))-3*r1^3*(-672*M^5+600*M^4*r1*ur1^2+M*r1^4*(40+446*ur1^2-267*ur1^4)+r1^5*(12-4*ur1^2+9*ur1^4)+2*M^2*r1^3*(-238-374*ur1^2+15*ur1^4)+12*M^3*r1^2*(76-16*ur1^2+53*ur1^4))+l1^2*r1*(360*M^5+r1^5*(127-193*e1^2+72*ur1^2)+4*M^4*r1*(-733+525*ur1^2)+2*M^3*r1^2*(1143+6974*ur1^2-1710*ur1^4)+M^2*r1^3*(1433-1895*ur1^2+54*ur1^4)+M*r1^4*(-1172-8171*ur1^2+1548*ur1^4))+6*l1^6*(128*M^2-2*M*r1*(47+210*ur1^2)+r1^2*(11-35*ur1^2+7*e1^2*(1+5*ur1^2))))-3*r1^5*(14*l1^8*(2*M-r1)*(2*M-r1*(3+10*ur1^2))+l1^4*r1^3*(728*M^3+4*M^2*r1*(-247+36*e1^2-374*ur1^2)+r1^3*(-228+184*e1^2-189*ur1^2)+2*M*r1^2*(384-96*e1^2+439*ur1^2))+2*(2*M-r1)*r1^7*(8*M^2-2*M*(r1+12*r1*ur1^2)-r1^2*(1+ur1^2+6*ur1^4))+l1^2*r1^5*(288*M^3+4*M^2*r1*(-86+9*e1^2-210*ur1^2)+r1^3*(-53+57*e1^2-79*ur1^2-18*ur1^4)+2*M*r1^2*(103-27*e1^2+250*ur1^2+18*ur1^4))+2*l1^6*r1*(248*M^3-4*M^2*r1*(81+7*e1^2+84*ur1^2)+2*M*r1^2*(117+7*ur1^2-35*ur1^4+7*e1^2*(2+5*ur1^2))+r1^3*(-67+91*ur1^2+70*ur1^4-7*e1^2*(3+10*ur1^2))))-a^2*r1^4*(-42*l1^8*(2*M-r1*(1+5*ur1^2))+l1^4*r1*(2400*M^4+r1^4*(-964+912*e1^2-375*ur1^2)+24*M^3*r1*(15-161*ur1^2)-12*M^2*r1^2*(354+791*ur1^2)+2*M*r1^3*(1459+4062*ur1^2))+3*r1^5*(-360*M^4+112*M^3*r1*(4+3*ur1^2)+M*r1^3*(14+227*ur1^2-111*ur1^4)+r1^4*(8+ur1^2+21*ur1^4)+2*M^2*r1^2*(-97-261*ur1^2+93*ur1^4))+l1^2*r1^3*(1872*M^4-12*M^3*r1*(9+482*ur1^2)+M*r1^3*(1103+5265*ur1^2-720*ur1^4)+r1^4*(-256+307*e1^2-217*ur1^2-54*ur1^4)+6*M^2*r1^2*(-344-819*ur1^2+240*ur1^4))+42*l1^6*(32*M^3-8*M^2*r1*(7+15*ur1^2)+2*M*r1^2*(16+37*ur1^2)+r1^3*(-4+16*ur1^2+5*ur1^4-e1^2*(4+15*ur1^2)))))*ΔQ^6*Δθ^2)/(3*r1^6*(a^2+r1*(-2*M+r1))^2)+((2*a^9*e1*l1*M*(52*M-5*r1)+a^10*(11*M^2+5*M*r1+(-1+e1^2)*r1^2)+6*a*e1*l1*r1^4*(3*M*r1^3*(36*M^2+r1^2*(-27+95*ur1^2)-2*M*r1*(8+95*ur1^2))+l1^2*r1*(604*M^3+12*M^2*r1*(-76+3*e1^2-89*ur1^2)+36*r1^3*(-1+e1^2-ur1^2)+3*M*r1^2*(317-14*e1^2+162*ur1^2))+l1^4*(88*M^2-36*r1^2-2*M*r1*(146+175*ur1^2)))+2*a^7*e1*l1*r1*(3*l1^2*(41*M+3*(-1+e1^2)*r1)+M*(-508*M^2+807*r1^2*ur1^2+4*M*r1*(49+386*ur1^2)))-a^8*(l1^2*(104*M^2+95*M*r1+(-50+51*e1^2)*r1^2)+r1*(-244*M^3+r1^3*(20-13*e1^2+ur1^2)+10*M*r1^2*(-1+34*ur1^2)+M^2*r1*(-193+574*ur1^2)))+2*a^5*e1*l1*r1^2*(-9*l1^4+l1^2*(-744*M^2+9*r1^2*(-7+7*e1^2-ur1^2)+3*M*r1*(291+598*ur1^2))+M*(808*M^3+10*M*r1^2*(8+101*ur1^2)-4*M^2*r1*(339+772*ur1^2)+r1^3*(22+2329*ur1^2)))+2*a^3*e1*l1*r1^3*(-6*l1^4*(35*M+9*r1)+3*l1^2*(332*M^3+18*r1^3*(-3+3*e1^2-ur1^2)+7*M*r1^2*(109+160*ur1^2)-4*M^2*r1*(222+299*ur1^2))+M*r1*(1368*M^3-4*M*r1^2*(69+491*ur1^2)-4*M^2*r1*(151+540*ur1^2)+r1^3*(-64+2377*ur1^2)))+a^6*r1*(l1^4*(-246*M+3*(10+7*e1^2)*r1)+r1*(-1108*M^4+r1^4*(-103+69*e1^2+10*ur1^2)+2*M^3*r1*(-106+1159*ur1^2)+M*r1^3*(52-1084*ur1^2+63*ur1^4)+M^2*r1^2*(619+362*ur1^2+135*ur1^4))+l1^2*(1016*M^3+M^2*r1*(322-3088*ur1^2)-9*M*r1^2*(101+321*ur1^2)+r1^3*(385+24*ur1^2+3*e1^2*(-140+9*ur1^2))))+a^4*r1^2*(-21*l1^6+r1*(1152*M^5-4*M^4*r1*(97+585*ur1^2)+r1^5*(-253+193*e1^2-6*ur1^2-27*ur1^4)+M^2*r1^3*(683+2720*ur1^2+9*ur1^4)+2*M*r1^4*(145-686*ur1^2+45*ur1^4)-2*M^3*r1^2*(714-329*ur1^2+135*ur1^4))+l1^4*(1488*M^2-12*M*r1*(119+299*ur1^2)+r1^2*(122-573*ur1^2+21*e1^2*(11+25*ur1^2)))+l1^2*(-1616*M^4+8*M^2*r1^2*(349+403*ur1^2)+4*M^3*r1*(129+1544*ur1^2)-M*r1^3*(2869+7422*ur1^2+720*ur1^4)+3*r1^4*(412+68*ur1^2-9*ur1^4+e1^2*(-453+54*ur1^2))))+a^2*r1^3*(105*l1^6*(4*M-r1*(2+5*ur1^2))+r1^3*(936*M^4-4*M^3*r1*(253+486*ur1^2)+r1^4*(-353+307*e1^2-112*ur1^2-81*ur1^4)+2*M^2*r1^2*(7+1088*ur1^2-27*ur1^4)+M*r1^3*(601-750*ur1^2+81*ur1^4))+l1^2*r1*(-360*M^4-4*M^3*r1*(517+267*ur1^2)-M*r1^3*(4441+6417*ur1^2+666*ur1^4)+2*M^2*r1^2*(2587+4752*ur1^2+720*ur1^4)+r1^4*(2069+765*ur1^2-81*ur1^4+12*e1^2*(-188+27*ur1^2)))+l1^4*(-1992*M^3+12*M^2*r1*(335+598*ur1^2)-2*M*r1^2*(1372+1677*ur1^2)+r1^3*(136-1846*ur1^2-525*ur1^4+3*e1^2*(274+525*ur1^2))))+r1^4*(-6*l1^6*(2*M-r1)*(44*M-r1*(102+175*ur1^2))+l1^2*r1^3*(-2088*M^3+4*M^2*r1*(865-189*e1^2+837*ur1^2)-2*M*r1^2*(1691+1155*ur1^2-27*ur1^4+27*e1^2*(-22+3*ur1^2))+r1^3*(1087+1179*ur1^2-135*ur1^4+3*e1^2*(-422+63*ur1^2)))+l1^4*r1*(-1968*M^3+4*M^2*r1*(749+39*e1^2+483*ur1^2)-2*M*r1^2*(1141-814*ur1^2-525*ur1^4+3*e1^2*(57+175*ur1^2))+r1^3*(638-1777*ur1^2-1050*ur1^4+6*e1^2*(102+175*ur1^2)))+r1^5*(72*M^3+4*M^2*r1*(-85+27*e1^2+81*ur1^2)-2*M*r1^2*(-260+81*e1^2+22*ur1^2-54*ur1^4)+r1^3*(171*e1^2-2*(92+88*ur1^2+27*ur1^4)))))*ΔQ^4*Δθ^4)/(3*r1^3*(a^2+r1*(-2*M+r1))^2)+((3*a^8*(15*M-(-4+e1^2)*r1)+18*a^7*e1*l1*(-M+(-1+e1^2)*r1)+6*a^5*e1*l1*r1*(-3*l1^2-24*M^2+3*r1^2*(-7+7*e1^2-ur1^2)+M*r1*(27+185*ur1^2))+6*a^3*e1*l1*r1^2*(60*M^3-6*l1^2*(8*M+3*r1)+18*r1^3*(-3+3*e1^2-ur1^2)-2*M^2*r1*(64+185*ur1^2)+M*r1^2*(103+364*ur1^2))+6*a*e1*l1*r1^3*(4*l1^2*(16*M^2-9*r1^2-M*r1*(58+69*ur1^2))+r1*(108*M^3+2*M^2*r1*(-68+18*e1^2-179*ur1^2)+36*r1^3*(-1+e1^2-ur1^2)+M*r1^2*(79-42*e1^2+179*ur1^2)))+a^6*(6*l1^2*(3*M+r1+e1^2*r1)+r1*(-102*M^2+M*r1*(47-288*ur1^2)+r1^2*(31-6*ur1^2+3*e1^2*(-4+3*ur1^2))))+a^2*r1^2*(18*l1^4*(16*M-r1*(8+23*ur1^2))+r1*(312*M^4-4*M^3*r1*(73+360*ur1^2)-3*M*r1^3*(-59+100*ur1^2+51*ur1^4)+2*M^2*r1^2*(-23+668*ur1^2+189*ur1^4)+r1^4*(-111-110*ur1^2-90*ur1^4+12*e1^2*(8+9*ur1^2)))+l1^2*(-360*M^3+2*M*r1^2*(223+36*ur1^2)+12*M^2*r1*(27+185*ur1^2)+r1^3*(-667-1443*ur1^2-396*ur1^4+54*e1^2*(12+23*ur1^2))))+r1^3*(-12*l1^4*(2*M-r1)*(16*M-3*r1*(14+23*ur1^2))+r1^3*(120*M^3+4*M^2*r1*(-65+27*e1^2+18*ur1^2)-2*M*r1^2*(-136-76*ur1^2-63*ur1^4+27*e1^2*(2+ur1^2))+r1^3*(-86-145*ur1^2-99*ur1^4+e1^2*(78+63*ur1^2)))+l1^2*r1*(-48*M^3+8*M^2*r1*(-52+9*e1^2-45*ur1^2)+r1^3*(-575-1344*ur1^2-810*ur1^4+36*e1^2*(14+23*ur1^2))+2*M*r1^2*(685+1026*ur1^2+396*ur1^4-6*e1^2*(19+69*ur1^2))))-a^4*r1*(6*l1^4+r1*(132*M^3-4*M^2*(r1+324*r1*ur1^2)+M*r1^2*(-15+584*ur1^2+189*ur1^4)+r1^3*(6+25*ur1^2+18*ur1^4-9*e1^2*(1+6*ur1^2)))-2*l1^2*(72*M^2-15*M*r1*(2+37*ur1^2)+r1^2*(-70-246*ur1^2+3*e1^2*(25+69*ur1^2)))))*ΔQ^2*Δθ^6)/(12*(a^2+r1*(-2*M+r1))^2)-(r1^2*(60*a^5*e1*l1*M-3*a^6*(10*e1^2*M+3*r1)-12*a^3*e1*l1*M*r1*(10*M+3*r1*(-2+7*ur1^2))-12*a*e1*l1*M*r1^3*(2*M+r1*(-1+21*ur1^2))+a^4*(-30*l1^2*M+r1*((24*M-17*r1)*r1+6*e1^2*M*(10*M-7*r1+21*r1*ur1^2)))+r1^4*(-48*M^3+4*M^2*r1*(13-9*e1^2+54*ur1^2)+r1^3*(1+2*ur1^2+9*ur1^4)+2*M*r1^2*(9*e1^2*(1+7*ur1^2)-8*(1+7*ur1^2+9*ur1^4)))+a^2*r1*(6*l1^2*M*(10*M+r1*(-5+21*ur1^2))+r1^2*(12*(1+2*e1^2)*M^2+r1^2*(-7+2*ur1^2+9*ur1^4)+2*M*r1*(4-54*ur1^2+3*e1^2*(1+42*ur1^2)))))*Δθ^8)/(48*(a^2+r1*(-2*M+r1))^2)))/(4*(l1^2+r1^2+(a^2*(2*M+r1))/r1)*ΔQ^2+(r1^2*(a^2+r1*(-2*M+r1+r1*ur1^2))*Δr^2)/(a^2+r1*(-2*M+r1))^2+(2*l1*r1^2*ur1*Δr*ΔR)/(a^2-2*M*r1+r1^2)+r1^2*Δθ^2)^(7/2);

Circular geodesic

For a circular geodesic, we have:

ur1=0
ut1=((a M+(Sqrt[M (r1^3)]))/((Sqrt[M r1])(Sqrt[(r1^2)-3M r1+2a(Sqrt[M r1])])))
uϕ1=((Sqrt[M r1])/(r1(Sqrt[(r1^2)-3M r1+2a(Sqrt[M r1])])))

along with
e1=((a M r1-2 M (Sqrt[M (r1^3)])+(Sqrt[M (r1^5)]))/(r1 (Sqrt[M r1 (-3 M r1+(r1^2)+2 a (Sqrt[M r1]))])))
l1=((M ((a^2) r1+(r1^3)-2 a (Sqrt[M (r1^3)])))/(r1 (Sqrt[M r1 (-3 M r1+(r1^2)+2 a (Sqrt[M r1]))])))

ΦsKerrCircular=(64*(r1^2+(a^2*(2*M+r1))/r1+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])))^3*ΔQ^6+(r1^6*Δr^6)/(a^2+r1*(-2*M+r1))^3+48*(a^2*(2*M+r1)+r1*(r1^2+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1]))))^2*ΔQ^4*Δθ^2+12*r1^3*(a^2*(2*M+r1)+r1*(r1^2+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1]))))*ΔQ^2*Δθ^4+r1^6*Δθ^6+Δr^4*((12*r1^2*(a^4*M*r1+2*a^3*Sqrt[M*r1^5]+r1^5*(-2*M+r1)+a^2*r1^2*(-2*M^2+M*r1+r1^2)+2*a*(-2*M^(3/2)*r1^(7/2)+Sqrt[M*r1^9]))*ΔQ^2)/((-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^2)+(3*r1^6*Δθ^2)/(a^2+r1*(-2*M+r1))^2)+Δr^2*((48*r1^2*(r1^2+(a^2*(2*M+r1))/r1+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])))^2*ΔQ^4)/(a^2+r1*(-2*M+r1))+(24*r1^3*(a^2*(2*M+r1)+r1*(r1^2+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1]))))*ΔQ^2*Δθ^2)/(a^2+r1*(-2*M+r1))+(3*r1^6*Δθ^4)/(a^2+r1*(-2*M+r1))))/(4*(r1^2+(a^2*(2*M+r1))/r1+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])))*ΔQ^2+(r1^2*Δr^2)/(a^2+r1*(-2*M+r1))+r1^2*Δθ^2)^(7/2)+((r1^5*(-a^2+M*r1)*Δr^7)/(2*(a^2+r1*(-2*M+r1))^4)+Δr^5*((-2*(2*a^6*M*r1^3+4*a^5*Sqrt[M*r1^9]+r1^8*(6*M^2-5*M*r1+r1^2)+a^4*r1^4*(-7*M^2+3*M*r1+2*r1^2)+a^2*r1^5*(6*M^3-5*M^2*r1-6*M*r1^2+3*r1^3)+2*a^3*(-7*M^(3/2)*r1^(11/2)+3*Sqrt[M*r1^13])+2*a*(6*M^(5/2)*r1^(13/2)-5*M^(3/2)*r1^(15/2)+Sqrt[M*r1^17]))*ΔQ^2)/(r1*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^3)-(r1^5*(3*a^2+r1*(-4*M+r1))*Δθ^2)/(2*(a^2+r1*(-2*M+r1))^3))+Δr^3*((-8*(a^4*M*r1+2*a^3*Sqrt[M*r1^5]+r1^5*(-2*M+r1)+a^2*r1^2*(-2*M^2+M*r1+r1^2)+2*a*(-2*M^(3/2)*r1^(7/2)+Sqrt[M*r1^9]))*(a^6*M*r1^3+2*a^5*Sqrt[M*r1^9]+a^4*r1^4*(-5*M^2+3*M*r1+r1^2)+r1^8*(6*M^2-7*M*r1+2*r1^2)+a^2*r1^5*(6*M^3-7*M^2*r1-3*M*r1^2+3*r1^3)+2*a^3*(-5*M^(3/2)*r1^(11/2)+3*Sqrt[M*r1^13])+2*a*(6*M^(5/2)*r1^(13/2)-7*M^(3/2)*r1^(15/2)+2*Sqrt[M*r1^17]))*ΔQ^4)/(r1^5*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^2)-(8*(a^6*M*r1^3+2*a^5*Sqrt[M*r1^9]+r1^8*(-2*M+r1)^2+a^4*r1^4*(-4*M^2+2*M*r1+r1^2)+a^2*r1^5*(4*M^3-4*M^2*r1-3*M*r1^2+2*r1^3)+4*a^3*(-2*M^(3/2)*r1^(11/2)+Sqrt[M*r1^13])+2*a*(4*M^(5/2)*r1^(13/2)-4*M^(3/2)*r1^(15/2)+Sqrt[M*r1^17]))*ΔQ^2*Δθ^2)/(r1*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^2)-(r1^5*(3*a^2+r1*(-5*M+2*r1))*Δθ^4)/(2*(a^2+r1*(-2*M+r1))^2))+Δr*((-32*(a^4*M*r1+2*a^3*Sqrt[M*r1^5]+r1^5*(-2*M+r1)+a^2*r1^2*(-2*M^2+M*r1+r1^2)+2*a*(-2*M^(3/2)*r1^(7/2)+Sqrt[M*r1^9]))^2*(a^4*M*r1^4*(-M+r1)+a^2*(M-r1)^2*r1^5*(2*M+r1)+r1^8*(2*M^2-3*M*r1+r1^2)+2*a^3*(-(M^(3/2)*r1^(11/2))+Sqrt[M*r1^13])+2*a*(2*M^(5/2)*r1^(13/2)-3*M^(3/2)*r1^(15/2)+Sqrt[M*r1^17]))*ΔQ^6)/(r1^9*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3*(a^2+r1*(-2*M+r1)))-(8*(a^4*M*r1+2*a^3*Sqrt[M*r1^5]+r1^5*(-2*M+r1)+a^2*r1^2*(-2*M^2+M*r1+r1^2)+2*a*(-2*M^(3/2)*r1^(7/2)+Sqrt[M*r1^9]))*(a^6*M*r1^3+2*a^5*Sqrt[M*r1^9]+a^4*r1^4*(-6*M^2+4*M*r1+r1^2)+r1^8*(8*M^2-10*M*r1+3*r1^2)+a^2*r1^5*(8*M^3-10*M^2*r1-3*M*r1^2+4*r1^3)+4*a^3*(-3*M^(3/2)*r1^(11/2)+2*Sqrt[M*r1^13])+2*a*(8*M^(5/2)*r1^(13/2)-10*M^(3/2)*r1^(15/2)+3*Sqrt[M*r1^17]))*ΔQ^4*Δθ^2)/(r1^5*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1)))-(2*(2*a^6*M*r1^3+4*a^5*Sqrt[M*r1^9]+a^4*r1^4*(-9*M^2+5*M*r1+2*r1^2)+r1^8*(10*M^2-11*M*r1+3*r1^2)+a^2*r1^5*(10*M^3-11*M^2*r1-6*M*r1^2+5*r1^3)+2*a^3*(-9*M^(3/2)*r1^(11/2)+5*Sqrt[M*r1^13])+a*(20*M^(5/2)*r1^(13/2)-22*M^(3/2)*r1^(15/2)+6*Sqrt[M*r1^17]))*ΔQ^2*Δθ^4)/(r1*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1)))-(r1^5*Δθ^6)/2))/(4*(r1^2+(a^2*(2*M+r1))/r1+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])))*ΔQ^2+(r1^2*Δr^2)/(a^2+r1*(-2*M+r1))+r1^2*Δθ^2)^(7/2)+((-32*M*(a^4*M*r1+2*a^3*Sqrt[M*r1^5]+r1^5*(-2*M+r1)+a^2*r1^2*(-2*M^2+M*r1+r1^2)+2*a*(-2*M^(3/2)*r1^(7/2)+Sqrt[M*r1^9]))^2*(2*a^7*M^(3/2)*r1^(7/2)+3*r1^11*(-2*M+r1)+a^6*M*r1^4*(3*M+7*r1)+6*a^2*r1^8*(-6*M^2+2*M*r1+r1^2)+a^4*r1^5*(-6*M^3-11*M^2*r1+25*M*r1^2+3*r1^3)+2*a^5*(-2*M^(5/2)*r1^(9/2)+7*M^(3/2)*r1^(11/2)+4*Sqrt[M*r1^13])+4*a^3*(-6*M^(5/2)*r1^(13/2)-M^(3/2)*r1^(15/2)+5*Sqrt[M*r1^17])+12*a*(-2*M^(3/2)*r1^(19/2)+Sqrt[M*r1^21]))*ΔQ^8)/(3*r1^13*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3)+((2*a*(3*M-2*r1)*r1^5*(M*r1)^(3/2)+2*a^5*Sqrt[M*r1^9]+a^4*r1^5*(-M+r1)+M^2*r1^7*(-M+r1)+2*a^2*r1^6*(2*M^2-3*M*r1+r1^2)+4*a^3*(-2*r1^4*(M*r1)^(3/2)+Sqrt[M*r1^13]))*Δr^8)/(4*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^5)+(16*(-6*a^11*M^(5/2)*(7*M-3*r1)*r1^(11/2)+a^12*M^3*r1^4*(-7*M+3*r1)+3*r1^16*(-2*M+r1)^2*(5*M^2-4*M*r1+r1^2)+2*a^9*M^(3/2)*r1^(13/2)*(129*M^3-123*M^2*r1-41*M*r1^2+30*r1^3)+a^10*M^2*r1^5*(43*M^3-41*M^2*r1-95*M*r1^2+45*r1^3)+3*a^2*r1^13*(300*M^5-576*M^4*r1+383*M^3*r1^2-91*M^2*r1^3-3*M*r1^4+3*r1^5)+a^8*M*r1^6*(-88*M^5+130*M^4*r1+580*M^3*r1^2-601*M^2*r1^3+36*M*r1^4+45*r1^5)+3*a^4*r1^10*(300*M^6-596*M^5*r1-M^4*r1^2+484*M^3*r1^3-263*M^2*r1^4+33*M*r1^5+3*r1^6)+a^6*r1^7*(60*M^7-120*M^6*r1-1229*M^5*r1^2+1907*M^4*r1^3-284*M^3*r1^4-450*M^2*r1^5+129*M*r1^6+3*r1^7)+2*a^7*(-264*M^(11/2)*r1^(15/2)+390*M^(9/2)*r1^(17/2)+239*M^(7/2)*r1^(19/2)-373*M^(5/2)*r1^(21/2)+71*M^(3/2)*r1^(23/2)+9*Sqrt[M*r1^25])+2*a^5*(180*M^(13/2)*r1^(17/2)-360*M^(11/2)*r1^(19/2)-611*M^(9/2)*r1^(21/2)+1187*M^(7/2)*r1^(23/2)-466*M^(5/2)*r1^(25/2)-23*M^(3/2)*r1^(27/2)+27*Sqrt[M*r1^29])+2*a^3*(600*M^(11/2)*r1^(23/2)-1176*M^(9/2)*r1^(25/2)+590*M^(7/2)*r1^(27/2)+94*M^(5/2)*r1^(29/2)-139*M^(3/2)*r1^(31/2)+27*Sqrt[M*r1^33])+6*a*(60*M^(9/2)*r1^(29/2)-112*M^(7/2)*r1^(31/2)+79*M^(5/2)*r1^(33/2)-25*M^(3/2)*r1^(35/2)+3*Sqrt[M*r1^37]))*ΔQ^6*Δθ^2)/(3*r1^8*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3)+(2*(-6*a^13*M^(5/2)*r1^(7/2)-3*a^12*M^2*r1^4*(M+9*r1)+4*a^11*M^(3/2)*r1^(9/2)*(4*M^2-M*r1-12*r1^2)+6*a^10*M*r1^5*(12*M^3+2*M^2*r1+3*M*r1^2-7*r1^3)+r1^14*(-2*M+r1)^2*(-111*M^3+174*M^2*r1-86*M*r1^2+13*r1^3)+a^8*r1^6*(-363*M^5+735*M^4*r1-399*M^3*r1^2+27*M^2*r1^3+53*M*r1^4-3*r1^5)+a^6*r1^7*(684*M^6-2226*M^5*r1+888*M^4*r1^2+1671*M^3*r1^3-1590*M^2*r1^4+369*M*r1^5+4*r1^6)+a^2*r1^11*(-2664*M^6+7692*M^5*r1-8314*M^4*r1^2+3903*M^3*r1^3-534*M^2*r1^4-139*M*r1^5+36*r1^6)+3*a^4*r1^8*(-148*M^7+616*M^6*r1+335*M^5*r1^2-2299*M^4*r1^3+2337*M^3*r1^4-892*M^2*r1^5+91*M*r1^6+10*r1^7)+a^9*(50*M^(9/2)*r1^(11/2)+140*M^(7/2)*r1^(13/2)-50*M^(5/2)*r1^(15/2)+52*M^(3/2)*r1^(17/2)-18*Sqrt[M*r1^19])+4*a^7*(-50*M^(11/2)*r1^(13/2)-238*M^(9/2)*r1^(15/2)+522*M^(7/2)*r1^(17/2)-367*M^(5/2)*r1^(19/2)+73*M^(3/2)*r1^(21/2)+6*Sqrt[M*r1^23])+2*a^5*(84*M^(13/2)*r1^(15/2)+1132*M^(11/2)*r1^(17/2)-3223*M^(9/2)*r1^(19/2)+2788*M^(7/2)*r1^(21/2)-596*M^(5/2)*r1^(23/2)-248*M^(3/2)*r1^(25/2)+90*Sqrt[M*r1^27])+4*a^3*(-444*M^(13/2)*r1^(19/2)+1428*M^(11/2)*r1^(21/2)-1223*M^(9/2)*r1^(23/2)-188*M^(7/2)*r1^(25/2)+743*M^(5/2)*r1^(27/2)-355*M^(3/2)*r1^(29/2)+54*Sqrt[M*r1^31])+6*a*(-296*M^(11/2)*r1^(25/2)+800*M^(9/2)*r1^(27/2)-858*M^(7/2)*r1^(29/2)+458*M^(5/2)*r1^(31/2)-122*M^(3/2)*r1^(33/2)+13*Sqrt[M*r1^35]))*ΔQ^4*Δθ^4)/(3*r1^5*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3*(a^2+r1*(-2*M+r1)))+((-6*a^9*M^(3/2)*r1^(7/2)-3*a^8*M*r1^4*(M+5*r1)+r1^10*(-2*M+r1)^2*(15*M^2-21*M*r1+4*r1^2)+a^6*r1^5*(27*M^3+45*M^2*r1-13*M*r1^2-3*r1^3)-2*a^4*r1^6*(36*M^4-9*M^3*r1+7*M^2*r1^2-5*M*r1^3+r1^4)+a^2*r1^7*(60*M^5-96*M^4*r1+59*M^3*r1^2+25*M^2*r1^3-29*M*r1^4+5*r1^5)-2*a^7*(-15*M^(5/2)*r1^(9/2)+5*M^(3/2)*r1^(11/2)+6*Sqrt[M*r1^13])+a^5*(-48*M^(7/2)*r1^(11/2)+58*M^(5/2)*r1^(13/2)+10*M^(3/2)*r1^(15/2)-8*Sqrt[M*r1^17])+2*a^3*(12*M^(9/2)*r1^(13/2)-68*M^(7/2)*r1^(15/2)+77*M^(5/2)*r1^(17/2)-43*M^(3/2)*r1^(19/2)+10*Sqrt[M*r1^21])+2*a*(60*M^(9/2)*r1^(17/2)-132*M^(7/2)*r1^(19/2)+119*M^(5/2)*r1^(21/2)-50*M^(3/2)*r1^(23/2)+8*Sqrt[M*r1^25]))*ΔQ^2*Δθ^6)/(3*r1^2*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1)))+(r1^2*(-6*a^5*Sqrt[M*r1^5]-3*a^4*r1^3*(M+r1)-2*a^2*r1^4*(-6*M^2+3*M*r1+r1^2)+r1^5*(-12*M^3+24*M^2*r1-11*M*r1^2+r1^3)-4*a^3*(-6*r1^2*(M*r1)^(3/2)+Sqrt[M*r1^9])+2*a*(4*r1^4*(M*r1)^(3/2)-12*r1^2*(M*r1)^(5/2)+Sqrt[M*r1^13]))*Δθ^8)/(24*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1)))+Δr^6*(((2*a^13*M^(3/2)*r1^(7/2)+5*a^12*M*r1^4*(M+r1)+M*(2*M-r1)^3*r1^12*(31*M^2-37*M*r1+8*r1^2)+2*a*M^(3/2)*(2*M-r1)^3*r1^(21/2)*(31*M^2-58*M*r1+24*r1^2)+a^10*r1^5*(-8*M^3-125*M^2*r1+80*M*r1^2+r1^3)+a^8*r1^6*(-103*M^4+847*M^3*r1-815*M^2*r1^2+166*M*r1^3+15*r1^4)+a^2*r1^9*(-2*M+r1)^2*(62*M^5-273*M^4*r1+128*M^3*r1^2+137*M^2*r1^3-86*M*r1^4+12*r1^5)+a^6*r1^7*(410*M^5-2383*M^4*r1+2828*M^3*r1^2-1008*M^2*r1^3-6*M*r1^4+39*r1^5)+a^4*r1^8*(-548*M^6+2968*M^5*r1-3931*M^4*r1^2+1646*M^3*r1^3+121*M^2*r1^4-223*M*r1^5+37*r1^6)+4*a^11*(-12*M^(5/2)*r1^(9/2)+10*M^(3/2)*r1^(11/2)+Sqrt[M*r1^13])+a^9*(282*M^(7/2)*r1^(11/2)-324*M^(5/2)*r1^(13/2)-28*M^(3/2)*r1^(15/2)+60*Sqrt[M*r1^17])+4*a^7*(-175*M^(9/2)*r1^(13/2)+214*M^(7/2)*r1^(15/2)+86*M^(5/2)*r1^(17/2)-154*M^(3/2)*r1^(19/2)+39*Sqrt[M*r1^21])+2*a^5*(396*M^(11/2)*r1^(15/2)-346*M^(9/2)*r1^(17/2)-826*M^(7/2)*r1^(19/2)+1200*M^(5/2)*r1^(21/2)-523*M^(3/2)*r1^(23/2)+74*Sqrt[M*r1^25])+4*a^3*(-84*M^(13/2)*r1^(17/2)-84*M^(11/2)*r1^(19/2)+731*M^(9/2)*r1^(21/2)-978*M^(7/2)*r1^(23/2)+546*M^(5/2)*r1^(25/2)-136*M^(3/2)*r1^(27/2)+12*Sqrt[M*r1^29]))*ΔQ^2)/(2*r1^2*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^6)-(r1*(a^8*(7*M-5*r1)*r1^4-10*a^9*Sqrt[M*r1^7]-2*a*M^(3/2)*(17*M-12*r1)*r1^(15/2)*(-2*M+r1)^2+M*r1^8*(-2*M+r1)^2*(19*M^2-21*M*r1+4*r1^2)-2*a^6*r1^5*(31*M^2-38*M*r1+11*r1^2)+a^4*r1^6*(183*M^3-305*M^2*r1+163*M*r1^2-29*r1^3)-2*a^2*r1^7*(106*M^4-213*M^3*r1+154*M^2*r1^2-49*M*r1^3+6*r1^4)+a^7*(84*M^(3/2)*r1^(9/2)-44*Sqrt[M*r1^11])+a^5*(-250*M^(5/2)*r1^(11/2)+248*M^(3/2)*r1^(13/2)-58*Sqrt[M*r1^15])-4*a^3*(-78*M^(7/2)*r1^(13/2)+109*M^(5/2)*r1^(15/2)-47*M^(3/2)*r1^(17/2)+6*Sqrt[M*r1^19]))*Δθ^2)/(8*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^6))+Δr^4*((2*(-6*a^17*M^(5/2)*r1^(7/2)+3*a^16*M^2*(7*M-9*r1)*r1^4-16*a^15*M^(3/2)*r1^(9/2)*(2*M^2-6*M*r1+3*r1^2)+3*r1^16*(-2*M+r1)^4*(-65*M^3+74*M^2*r1-26*M*r1^2+3*r1^3)-6*a^14*M*r1^5*(16*M^3+15*M^2*r1-30*M*r1^2+7*r1^3)-3*a^12*r1^6*(89*M^5-1045*M^4*r1+1090*M^3*r1^2-224*M^2*r1^3-35*M*r1^4+r1^5)-3*a^2*(2*M-r1)^3*r1^13*(780*M^5-1740*M^4*r1+1035*M^3*r1^2-52*M^2*r1^3-97*M*r1^4+18*r1^5)+3*a^10*r1^7*(872*M^6-5676*M^5*r1+6230*M^4*r1^2-997*M^3*r1^3-1034*M^2*r1^4+307*M*r1^5+2*r1^6)+3*a^8*r1^8*(-2216*M^7+13536*M^6*r1-15174*M^5*r1^2-994*M^4*r1^3+8754*M^3*r1^4-4123*M^2*r1^5+516*M*r1^6+21*r1^7)+3*a^4*r1^10*(-2*M+r1)^2*(-260*M^7+1432*M^6*r1+1643*M^5*r1^2-7299*M^4*r1^3+5966*M^3*r1^4-1534*M^2*r1^5-33*M*r1^6+41*r1^7)+12*a^6*r1^9*(616*M^8-3836*M^7*r1+3614*M^6*r1^2+3939*M^5*r1^3-8102*M^4*r1^4+4813*M^3*r1^5-1141*M^2*r1^6+54*M*r1^7+11*r1^8)+a^13*(658*M^(9/2)*r1^(11/2)-980*M^(7/2)*r1^(13/2)+88*M^(5/2)*r1^(15/2)+180*M^(3/2)*r1^(17/2)-18*Sqrt[M*r1^19])+4*a^11*(-756*M^(11/2)*r1^(13/2)+783*M^(9/2)*r1^(15/2)+1018*M^(7/2)*r1^(17/2)-1229*M^(5/2)*r1^(19/2)+283*M^(3/2)*r1^(21/2)+9*Sqrt[M*r1^23])+2*a^9*(3176*M^(13/2)*r1^(15/2)-696*M^(11/2)*r1^(17/2)-14874*M^(9/2)*r1^(19/2)+17798*M^(7/2)*r1^(21/2)-6361*M^(5/2)*r1^(23/2)+158*M^(3/2)*r1^(25/2)+189*Sqrt[M*r1^27])+8*a^7*(-808*M^(15/2)*r1^(17/2)-1432*M^(13/2)*r1^(19/2)+10622*M^(11/2)*r1^(21/2)-13660*M^(9/2)*r1^(23/2)+6140*M^(7/2)*r1^(25/2)-214*M^(5/2)*r1^(27/2)-525*M^(3/2)*r1^(29/2)+99*Sqrt[M*r1^31])+2*a^5*(1296*M^(17/2)*r1^(19/2)+11136*M^(15/2)*r1^(21/2)-55528*M^(13/2)*r1^(23/2)+74792*M^(11/2)*r1^(25/2)-34135*M^(9/2)*r1^(27/2)-5782*M^(7/2)*r1^(29/2)+10586*M^(5/2)*r1^(31/2)-3442*M^(3/2)*r1^(33/2)+369*Sqrt[M*r1^35])+4*a^3*(-3120*M^(17/2)*r1^(23/2)+13824*M^(15/2)*r1^(25/2)-16920*M^(13/2)*r1^(27/2)+808*M^(11/2)*r1^(29/2)+14221*M^(9/2)*r1^(31/2)-12954*M^(7/2)*r1^(33/2)+5245*M^(5/2)*r1^(35/2)-1037*M^(3/2)*r1^(37/2)+81*Sqrt[M*r1^39])+6*a*(-2080*M^(15/2)*r1^(29/2)+7008*M^(13/2)*r1^(31/2)-10000*M^(11/2)*r1^(33/2)+7824*M^(9/2)*r1^(35/2)-3618*M^(7/2)*r1^(37/2)+986*M^(5/2)*r1^(39/2)-146*M^(3/2)*r1^(41/2)+9*Sqrt[M*r1^43]))*ΔQ^4)/(3*r1^5*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3*(a^2+r1*(-2*M+r1))^5)+(2*(2*a^12*M^2*r1^4-14*a^11*M^(3/2)*(M-r1)*r1^(9/2)+a^10*M*r1^5*(M^2-40*M*r1+27*r1^2)+(2*M-r1)^3*r1^12*(25*M^3-36*M^2*r1+15*M*r1^2-2*r1^3)+a^8*r1^6*(-79*M^4+371*M^3*r1-340*M^2*r1^2+73*M*r1^3+5*r1^4)+a^2*r1^9*(-2*M+r1)^2*(50*M^5-185*M^4*r1+97*M^3*r1^2+78*M^2*r1^3-63*M*r1^4+11*r1^5)+a^6*r1^7*(290*M^5-1239*M^4*r1+1394*M^3*r1^2-514*M^2*r1^3+12*M*r1^4+17*r1^5)+a^4*r1^8*(-404*M^6+1784*M^5*r1-2283*M^4*r1^2+1018*M^3*r1^3+8*M^2*r1^4-114*M*r1^5+21*r1^6)+2*a^9*(53*M^(7/2)*r1^(11/2)-61*M^(5/2)*r1^(13/2)-2*M^(3/2)*r1^(15/2)+10*Sqrt[M*r1^17])+4*a^7*(-75*M^(9/2)*r1^(13/2)+82*M^(7/2)*r1^(15/2)+43*M^(5/2)*r1^(17/2)-67*M^(3/2)*r1^(19/2)+17*Sqrt[M*r1^21])+4*a^5*(94*M^(11/2)*r1^(15/2)-49*M^(9/2)*r1^(17/2)-249*M^(7/2)*r1^(19/2)+325*M^(5/2)*r1^(21/2)-142*M^(3/2)*r1^(23/2)+21*Sqrt[M*r1^25])+2*a^3*(-88*M^(13/2)*r1^(17/2)-184*M^(11/2)*r1^(19/2)+1006*M^(9/2)*r1^(21/2)-1308*M^(7/2)*r1^(23/2)+761*M^(5/2)*r1^(25/2)-209*M^(3/2)*r1^(27/2)+22*Sqrt[M*r1^29])+2*a*(200*M^(13/2)*r1^(21/2)-676*M^(11/2)*r1^(23/2)+922*M^(9/2)*r1^(25/2)-651*M^(7/2)*r1^(27/2)+251*M^(5/2)*r1^(29/2)-50*M^(3/2)*r1^(31/2)+4*Sqrt[M*r1^33]))*ΔQ^2*Δθ^2)/(r1^2*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^5)+(r1^4*(9*a^4+5*r1^2*(9*M^2-10*M*r1+2*r1^2)+a^2*(-48*M*r1+34*r1^2))*Δθ^4)/(24*(a^2+r1*(-2*M+r1))^3))+Δr^2*((8*(-2*a^16*M^3*r1^4*(7*M+3*r1)-12*a^15*M^(5/2)*r1^(11/2)*(7*M+3*r1)+3*r1^18*(-2*M+r1)^4*(15*M^2-10*M*r1+3*r1^2)+a^14*M^2*r1^5*(157*M^3-44*M^2*r1-223*M*r1^2-90*r1^3)+2*a^13*M^(3/2)*r1^(13/2)*(471*M^3-132*M^2*r1-181*M*r1^2-60*r1^3)+3*a^2*(2*M-r1)^3*r1^15*(450*M^4-561*M^3*r1+190*M^2*r1^2-5*M*r1^3-10*r1^4)-a^12*M*r1^6*(696*M^5-660*M^4*r1-2183*M^3*r1^2+646*M^2*r1^3+423*M*r1^4+90*r1^5)+3*a^4*r1^12*(-2*M+r1)^2*(900*M^6-1612*M^5*r1-947*M^4*r1^2+2030*M^3*r1^3-811*M^2*r1^4+90*M*r1^5+10*r1^6)-4*a^7*M^(3/2)*r1^(19/2)*(2496*M^6-5496*M^5*r1-2716*M^4*r1^2+9714*M^3*r1^3-5313*M^2*r1^4+737*M*r1^5+48*r1^6)-a^10*r1^7*(-1528*M^7+2424*M^6*r1+8994*M^5*r1^2-9460*M^4*r1^3+15*M^3*r1^4+576*M^2*r1^5+237*M*r1^6+6*r1^7)+a^8*r1^8*(-1664*M^8+3664*M^7*r1+19616*M^6*r1^2-34676*M^5*r1^3+10300*M^4*r1^4+4238*M^3*r1^5-1533*M^2*r1^6-30*M*r1^7-15*r1^8)+a^6*M*r1^9*(720*M^8-2016*M^7*r1-22552*M^6*r1^2+53192*M^5*r1^3-25179*M^4*r1^4-13528*M^3*r1^5+14315*M^2*r1^6-3882*M*r1^7+330*r1^8)-4*a^11*(1044*M^(11/2)*r1^(15/2)-990*M^(9/2)*r1^(17/2)-535*M^(7/2)*r1^(19/2)+206*M^(5/2)*r1^(21/2)+94*M^(3/2)*r1^(23/2)+9*Sqrt[M*r1^25])-2*a^9*(-4584*M^(13/2)*r1^(17/2)+7272*M^(11/2)*r1^(19/2)+2670*M^(9/2)*r1^(21/2)-5376*M^(7/2)*r1^(23/2)+959*M^(5/2)*r1^(25/2)+104*M^(3/2)*r1^(27/2)+45*Sqrt[M*r1^29])+2*a^5*(2160*M^(17/2)*r1^(21/2)-6048*M^(15/2)*r1^(23/2)-9448*M^(13/2)*r1^(25/2)+31592*M^(11/2)*r1^(27/2)-25625*M^(9/2)*r1^(29/2)+7004*M^(7/2)*r1^(31/2)+629*M^(5/2)*r1^(33/2)-644*M^(3/2)*r1^(35/2)+90*Sqrt[M*r1^37])+4*a^3*(3600*M^(15/2)*r1^(27/2)-9984*M^(13/2)*r1^(29/2)+9224*M^(11/2)*r1^(31/2)-2176*M^(9/2)*r1^(33/2)-1827*M^(7/2)*r1^(35/2)+1472*M^(5/2)*r1^(37/2)-418*M^(3/2)*r1^(39/2)+45*Sqrt[M*r1^41])+6*a*(720*M^(13/2)*r1^(33/2)-1952*M^(11/2)*r1^(35/2)+2248*M^(9/2)*r1^(37/2)-1416*M^(7/2)*r1^(39/2)+517*M^(5/2)*r1^(41/2)-104*M^(3/2)*r1^(43/2)+9*Sqrt[M*r1^45]))*ΔQ^6)/(3*r1^8*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3*(a^2+r1*(-2*M+r1))^3)+(2*(-6*a^14*M^2*r1^3-24*a^13*M^(3/2)*r1^(9/2)+2*a^12*M*r1^4*(2*M^2-3*M*r1-18*r1^2)-3*(2*M-r1)^3*r1^14*(37*M^2-40*M*r1+13*r1^2)+a^10*r1^5*(231*M^4-222*M^3*r1+83*M^2*r1^2-36*M*r1^3-6*r1^4)+3*a^2*r1^11*(-2*M+r1)^2*(-444*M^4+722*M^3*r1-275*M^2*r1^2-60*M*r1^3+43*r1^4)-3*a^8*r1^6*(334*M^5-515*M^4*r1-186*M^3*r1^2+391*M^2*r1^3-116*M*r1^4+2*r1^5)+a^6*r1^7*(1588*M^6-3324*M^5*r1-3339*M^4*r1^2+8260*M^3*r1^3-4524*M^2*r1^4+672*M*r1^5+57*r1^6)+a^4*r1^8*(-888*M^7+2340*M^6*r1+7022*M^5*r1^2-18513*M^4*r1^3+14472*M^3*r1^4-4156*M^2*r1^5-18*M*r1^6+147*r1^7)-8*a^11*(-2*M^(5/2)*r1^(11/2)+3*M^(3/2)*r1^(13/2)+3*Sqrt[M*r1^15])-4*a^9*(-231*M^(7/2)*r1^(13/2)+222*M^(5/2)*r1^(15/2)-62*M^(3/2)*r1^(17/2)+6*Sqrt[M*r1^19])+12*a^7*(-334*M^(9/2)*r1^(15/2)+515*M^(7/2)*r1^(17/2)-197*M^(5/2)*r1^(19/2)-23*M^(3/2)*r1^(21/2)+19*Sqrt[M*r1^23])+4*a^5*(1588*M^(11/2)*r1^(17/2)-3324*M^(9/2)*r1^(19/2)+1659*M^(7/2)*r1^(21/2)+565*M^(5/2)*r1^(23/2)-675*M^(3/2)*r1^(25/2)+147*Sqrt[M*r1^27])+4*a^3*(-888*M^(13/2)*r1^(19/2)+2340*M^(11/2)*r1^(21/2)-910*M^(9/2)*r1^(23/2)-1941*M^(7/2)*r1^(25/2)+2247*M^(5/2)*r1^(27/2)-901*M^(3/2)*r1^(29/2)+129*Sqrt[M*r1^31])+12*a*(-296*M^(11/2)*r1^(25/2)+772*M^(9/2)*r1^(27/2)-818*M^(7/2)*r1^(29/2)+439*M^(5/2)*r1^(31/2)-119*M^(3/2)*r1^(33/2)+13*Sqrt[M*r1^35]))*ΔQ^4*Δθ^2)/(3*r1^5*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^3)+((-18*a^11*M^(3/2)*r1^(7/2)+3*a^10*M*(M-15*r1)*r1^4+r1^11*(-2*M+r1)^2*(-294*M^3+498*M^2*r1-259*M*r1^2+41*r1^3)+2*a^6*r1^6*(-405*M^4+789*M^3*r1-648*M^2*r1^2+162*M*r1^3+4*r1^4)+6*a^4*r1^7*(284*M^5-818*M^4*r1+823*M^3*r1^2-279*M^2*r1^3-10*M*r1^4+14*r1^5)+a^2*r1^8*(-1176*M^6+4224*M^5*r1-4466*M^4*r1^2+750*M^3*r1^3+1293*M^2*r1^4-719*M*r1^5+108*r1^6)+a^8*(120*M^3*r1^5+43*M*r1^7-9*r1^8)+a^9*(48*M^(5/2)*r1^(9/2)+22*M^(3/2)*r1^(11/2)-36*Sqrt[M*r1^13])+4*a^7*(39*M^(7/2)*r1^(11/2)-42*M^(5/2)*r1^(13/2)+6*M^(3/2)*r1^(15/2)+8*Sqrt[M*r1^17])+12*a^5*(-52*M^(9/2)*r1^(13/2)-13*M^(7/2)*r1^(15/2)+140*M^(5/2)*r1^(17/2)-116*M^(3/2)*r1^(19/2)+28*Sqrt[M*r1^21])+2*a^3*(264*M^(11/2)*r1^(15/2)+992*M^(9/2)*r1^(17/2)-3294*M^(7/2)*r1^(19/2)+3276*M^(5/2)*r1^(21/2)-1387*M^(3/2)*r1^(23/2)+216*Sqrt[M*r1^25])+2*a*(-1176*M^(11/2)*r1^(19/2)+3432*M^(9/2)*r1^(21/2)-4034*M^(7/2)*r1^(23/2)+2376*M^(5/2)*r1^(25/2)-699*M^(3/2)*r1^(27/2)+82*Sqrt[M*r1^29]))*ΔQ^2*Δθ^4)/(6*r1^2*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^3)+(r1^2*(-6*a^5*Sqrt[M*r1^5]-3*a^4*r1^3*(5*M+r1)+2*a^2*r1^4*(39*M^2-33*M*r1+4*r1^2)+r1^5*(-96*M^3+162*M^2*r1-79*M*r1^2+11*r1^3)+4*a^3*(3*r1^2*(M*r1)^(3/2)+4*Sqrt[M*r1^9])+22*a*(-2*r1^4*(M*r1)^(3/2)+Sqrt[M*r1^13]))*Δθ^6)/(24*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^2)))/(4*(r1^2+(a^2*(2*M+r1))/r1+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])))*ΔQ^2+(r1^2*Δr^2)/(a^2+r1*(-2*M+r1))+r1^2*Δθ^2)^(7/2)+(-(r1*(a^6*r1^4+2*a^7*Sqrt[M*r1^5]+M^2*r1^6*(2*M^2-2*M*r1+r1^2)-4*a*M^(3/2)*r1^(11/2)*(5*M^2-6*M*r1+2*r1^2)+a^4*r1^4*(2*M^2-6*M*r1+3*r1^2)+a^2*r1^5*(-8*M^3+19*M^2*r1-16*M*r1^2+4*r1^3)+2*a^5*(-7*M^(3/2)*r1^(7/2)+3*Sqrt[M*r1^9])+a^3*(32*M^(5/2)*r1^(9/2)-30*M^(3/2)*r1^(11/2)+8*Sqrt[M*r1^13]))*Δr^9)/(8*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^6)+Δr^7*(((6*a^17*M^(3/2)*r1^(7/2)+3*a^16*M*r1^4*(-3*M+5*r1)-2*a*M^(3/2)*r1^(25/2)*(-2*M+r1)^4*(89*M^3-148*M^2*r1+100*M*r1^2-26*r1^3)+a^14*r1^5*(61*M^3-97*M^2*r1+21*M*r1^2+3*r1^3)-M*r1^14*(-2*M+r1)^4*(89*M^3-73*M^2*r1+10*M*r1^2+4*r1^3)+a^12*r1^6*(-3*M^4-423*M^3*r1+547*M^2*r1^2-211*M*r1^3+6*r1^4)-3*a^10*r1^7*(355*M^5-1835*M^4*r1+2321*M^3*r1^2-1189*M^2*r1^3+198*M*r1^4+10*r1^5)+3*a^4*r1^10*(-2*M+r1)^2*(404*M^6-1924*M^5*r1+2209*M^4*r1^2-1003*M^3*r1^3+11*M^2*r1^4+141*M*r1^5-34*r1^6)-a^2*(2*M-r1)^3*r1^11*(178*M^6-835*M^5*r1+507*M^4*r1^2+85*M^3*r1^3-235*M^2*r1^4+120*M*r1^5-24*r1^6)-5*a^8*r1^8*(-784*M^6+3964*M^5*r1-5853*M^4*r1^2+3893*M^3*r1^3-1127*M^2*r1^4+51*M*r1^5+24*r1^6)+a^6*r1^9*(-6312*M^7+33840*M^6*r1-56830*M^5*r1^2+45310*M^4*r1^3-17505*M^3*r1^4+1901*M^2*r1^5+685*M*r1^6-165*r1^7)+6*a^15*(-3*M^(5/2)*r1^(9/2)-M^(3/2)*r1^(11/2)+2*Sqrt[M*r1^13])+a^13*(-270*M^(7/2)*r1^(11/2)+362*M^(5/2)*r1^(13/2)-200*M^(3/2)*r1^(15/2)+24*Sqrt[M*r1^17])-6*a^11*(-345*M^(9/2)*r1^(13/2)+491*M^(7/2)*r1^(15/2)-234*M^(5/2)*r1^(17/2)-2*M^(3/2)*r1^(19/2)+20*Sqrt[M*r1^21])-30*a^9*(208*M^(11/2)*r1^(15/2)-325*M^(9/2)*r1^(17/2)+126*M^(7/2)*r1^(19/2)+78*M^(5/2)*r1^(21/2)-75*M^(3/2)*r1^(23/2)+16*Sqrt[M*r1^25])-2*a^7*(-4824*M^(13/2)*r1^(17/2)+7480*M^(11/2)*r1^(19/2)-310*M^(9/2)*r1^(21/2)-7470*M^(7/2)*r1^(23/2)+6805*M^(5/2)*r1^(25/2)-2473*M^(3/2)*r1^(27/2)+330*Sqrt[M*r1^29])-6*a^5*(1264*M^(15/2)*r1^(19/2)-1432*M^(13/2)*r1^(21/2)-2376*M^(11/2)*r1^(23/2)+6390*M^(9/2)*r1^(25/2)-5975*M^(7/2)*r1^(27/2)+2853*M^(5/2)*r1^(29/2)-694*M^(3/2)*r1^(31/2)+68*Sqrt[M*r1^33])-6*a^3*(-400*M^(17/2)*r1^(21/2)-336*M^(15/2)*r1^(23/2)+3800*M^(13/2)*r1^(25/2)-7192*M^(11/2)*r1^(27/2)+6875*M^(9/2)*r1^(29/2)-3825*M^(7/2)*r1^(31/2)+1248*M^(5/2)*r1^(33/2)-220*M^(3/2)*r1^(35/2)+16*Sqrt[M*r1^37]))*ΔQ^2)/(4*r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^8)-((23*a^10*(M-r1)^2*r1^5+6*a^13*Sqrt[M*r1^7]+a^12*r1^4*(-M+3*r1)+2*a*M^(3/2)*(2*M-r1)^3*r1^(19/2)*(57*M^2-74*M*r1+26*r1^2)-M*(2*M-r1)^3*r1^10*(19*M^3-7*M^2*r1-6*M*r1^2+4*r1^3)+a^8*r1^6*(-173*M^3+354*M^2*r1-286*M*r1^2+75*r1^3)+a^2*r1^9*(-2*M+r1)^2*(175*M^4-290*M^3*r1+263*M^2*r1^2-124*M*r1^3+24*r1^4)+a^6*r1^7*(585*M^4-1354*M^3*r1+1398*M^2*r1^2-666*M*r1^3+117*r1^4)+a^4*r1^8*(-958*M^5+2471*M^4*r1-2992*M^3*r1^2+1952*M^2*r1^3-649*M*r1^4+86*r1^5)+a^11*(-94*M^(3/2)*r1^(9/2)+46*Sqrt[M*r1^11])+6*a^9*(97*M^(5/2)*r1^(11/2)-97*M^(3/2)*r1^(13/2)+25*Sqrt[M*r1^15])+2*a^7*(-915*M^(7/2)*r1^(13/2)+1373*M^(5/2)*r1^(15/2)-695*M^(3/2)*r1^(17/2)+117*Sqrt[M*r1^19])+2*a^5*(1546*M^(9/2)*r1^(15/2)-3055*M^(7/2)*r1^(17/2)+2259*M^(5/2)*r1^(19/2)-731*M^(3/2)*r1^(21/2)+86*Sqrt[M*r1^23])+6*a^3*(-444*M^(11/2)*r1^(17/2)+1072*M^(9/2)*r1^(19/2)-1019*M^(7/2)*r1^(21/2)+469*M^(5/2)*r1^(23/2)-102*M^(3/2)*r1^(25/2)+8*Sqrt[M*r1^27]))*Δθ^2)/(16*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^8))+Δr^5*(((18*a^18*M^3*r1^4+6*a^17*M^(5/2)*r1^(9/2)*(11*M+27*r1)-9*a^16*M^2*r1^5*(25*M^2-18*M*r1-57*r1^2)-8*a^15*M^(3/2)*r1^(11/2)*(136*M^3+122*M^2*r1-27*M*r1^2-99*r1^3)-6*a*M^(3/2)*r1^(31/2)*(-2*M+r1)^4*(390*M^3-522*M^2*r1+283*M*r1^2-61*r1^3)-3*M*r1^17*(-2*M+r1)^4*(195*M^3-207*M^2*r1+83*M*r1^2-9*r1^3)+6*a^14*M*r1^6*(272*M^4-671*M^3*r1-402*M^2*r1^2+115*M*r1^3+108*r1^4)-3*a^2*(2*M-r1)^3*r1^14*(2340*M^6-5364*M^5*r1+3857*M^4*r1^2-1042*M^3*r1^3-148*M^2*r1^4+136*M*r1^5-21*r1^6)+3*a^12*r1^7*(-2507*M^6+10242*M^5*r1-3545*M^4*r1^2+357*M^3*r1^3-1685*M^2*r1^4+511*M*r1^5+15*r1^6)+3*a^10*r1^8*(6936*M^7-36444*M^6*r1+30758*M^5*r1^2-8139*M^4*r1^3+2588*M^3*r1^4-768*M^2*r1^5-178*M*r1^6+39*r1^7)+3*a^8*r1^9*(-11000*M^8+67256*M^7*r1-73170*M^6*r1^2+10404*M^5*r1^3+24700*M^4*r1^4-20221*M^3*r1^5+7654*M^2*r1^6-1205*M*r1^7+6*r1^8)-3*a^4*r1^11*(-2*M+r1)^2*(780*M^8-4980*M^7*r1-5129*M^6*r1^2+24598*M^5*r1^3-24779*M^4*r1^4+11989*M^3*r1^5-2543*M^2*r1^6-41*M*r1^7+69*r1^8)+6*a^6*r1^10*(4592*M^9-31224*M^8*r1+31916*M^7*r1^2+22214*M^6*r1^3-61642*M^5*r1^4+50758*M^4*r1^5-22078*M^3*r1^6+4921*M^2*r1^7-334*M*r1^8-33*r1^9)+2*a^13*(3347*M^(11/2)*r1^(13/2)+543*M^(9/2)*r1^(15/2)-2076*M^(7/2)*r1^(17/2)-2204*M^(5/2)*r1^(19/2)+759*M^(3/2)*r1^(21/2)+135*Sqrt[M*r1^23])+2*a^11*(-10296*M^(13/2)*r1^(15/2)+594*M^(11/2)*r1^(17/2)+19010*M^(9/2)*r1^(19/2)-7950*M^(7/2)*r1^(21/2)+1437*M^(5/2)*r1^(23/2)-1466*M^(3/2)*r1^(25/2)+351*Sqrt[M*r1^27])+2*a^9*(17048*M^(15/2)*r1^(17/2)+5344*M^(13/2)*r1^(19/2)-84534*M^(11/2)*r1^(21/2)+89600*M^(9/2)*r1^(23/2)-45645*M^(7/2)*r1^(25/2)+15432*M^(5/2)*r1^(27/2)-2759*M^(3/2)*r1^(29/2)+54*Sqrt[M*r1^31])-4*a^7*(7280*M^(17/2)*r1^(19/2)+13536*M^(15/2)*r1^(21/2)-94884*M^(13/2)*r1^(23/2)+129228*M^(11/2)*r1^(25/2)-82860*M^(9/2)*r1^(27/2)+27864*M^(7/2)*r1^(29/2)-2813*M^(5/2)*r1^(31/2)-1176*M^(3/2)*r1^(33/2)+297*Sqrt[M*r1^35])+2*a^5*(5040*M^(19/2)*r1^(21/2)+39120*M^(17/2)*r1^(23/2)-207640*M^(15/2)*r1^(25/2)+307728*M^(13/2)*r1^(27/2)-202389*M^(11/2)*r1^(29/2)+44499*M^(9/2)*r1^(31/2)+24018*M^(7/2)*r1^(33/2)-20508*M^(5/2)*r1^(35/2)+5881*M^(3/2)*r1^(37/2)-621*Sqrt[M*r1^39])-2*a^3*(18720*M^(19/2)*r1^(25/2)-87840*M^(17/2)*r1^(27/2)+116688*M^(15/2)*r1^(29/2)-28304*M^(13/2)*r1^(31/2)-76542*M^(11/2)*r1^(33/2)+94658*M^(9/2)*r1^(35/2)-53246*M^(7/2)*r1^(37/2)+16683*M^(5/2)*r1^(39/2)-2782*M^(3/2)*r1^(41/2)+189*Sqrt[M*r1^43]))*ΔQ^4)/(3*r1^6*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3*(a^2+r1*(-2*M+r1))^6)+((18*a^15*M^(3/2)*r1^(7/2)+a^14*M*r1^4*(-19*M+45*r1)+a^12*r1^5*(109*M^3-334*M^2*r1+126*M*r1^2+9*r1^3)+(2*M-r1)^3*r1^13*(279*M^4-307*M^3*r1+86*M^2*r1^2+12*M*r1^3-4*r1^4)+a^10*r1^6*(89*M^4-122*M^3*r1+207*M^2*r1^2-209*M*r1^3+29*r1^4)-a^8*r1^7*(1909*M^5-6718*M^4*r1+7369*M^3*r1^2-3744*M^2*r1^3+703*M*r1^4+11*r1^5)+a^6*r1^8*(5158*M^6-21091*M^5*r1+27399*M^4*r1^2-16498*M^3*r1^3+4275*M^2*r1^4-60*M*r1^5-113*r1^6)+a^2*r1^10*(-2*M+r1)^2*(558*M^6-2213*M^5*r1+1344*M^4*r1^2+420*M^3*r1^3-687*M^2*r1^4+240*M*r1^5-32*r1^6)-a^4*r1^9*(5644*M^7-25732*M^6*r1+36945*M^5*r1^2-24015*M^4*r1^3+6207*M^3*r1^4+756*M^2*r1^5-757*M*r1^6+118*r1^7)+a^13*(-90*M^(5/2)*r1^(9/2)+20*M^(3/2)*r1^(11/2)+36*Sqrt[M*r1^13])+2*a^11*(-103*M^(7/2)*r1^(11/2)+168*M^(5/2)*r1^(13/2)-210*M^(3/2)*r1^(15/2)+58*Sqrt[M*r1^17])-2*a^9*(-1143*M^(9/2)*r1^(13/2)+1472*M^(7/2)*r1^(15/2)-918*M^(5/2)*r1^(17/2)+192*M^(3/2)*r1^(19/2)+22*Sqrt[M*r1^21])-2*a^7*(2946*M^(11/2)*r1^(15/2)-3598*M^(9/2)*r1^(17/2)+542*M^(7/2)*r1^(19/2)+1632*M^(5/2)*r1^(21/2)-1143*M^(3/2)*r1^(23/2)+226*Sqrt[M*r1^25])-2*a^5*(-3236*M^(13/2)*r1^(17/2)+2346*M^(11/2)*r1^(19/2)+5472*M^(9/2)*r1^(21/2)-9888*M^(7/2)*r1^(23/2)+6597*M^(5/2)*r1^(25/2)-2028*M^(3/2)*r1^(27/2)+236*Sqrt[M*r1^29])-2*a^3*(1320*M^(15/2)*r1^(19/2)+2048*M^(13/2)*r1^(21/2)-12114*M^(11/2)*r1^(23/2)+17502*M^(9/2)*r1^(25/2)-12453*M^(7/2)*r1^(27/2)+4752*M^(5/2)*r1^(29/2)-906*M^(3/2)*r1^(31/2)+64*Sqrt[M*r1^33])+2*a*(2232*M^(15/2)*r1^(23/2)-7124*M^(13/2)*r1^(25/2)+9642*M^(11/2)*r1^(27/2)-6967*M^(9/2)*r1^(29/2)+2736*M^(7/2)*r1^(31/2)-492*M^(5/2)*r1^(33/2)+2*M^(3/2)*r1^(35/2)+8*Sqrt[M*r1^37]))*ΔQ^2*Δθ^2)/(4*r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^6)+((18*a^11*Sqrt[M*r1^7]+9*a^10*r1^4*(M+r1)+a^8*r1^5*(-114*M^2-9*M*r1+5*r1^2)+a^6*r1^6*(597*M^3-471*M^2*r1+245*M*r1^2-79*r1^3)+r1^9*(-2*M+r1)^2*(-132*M^4+75*M^3*r1+41*M^2*r1^2-32*M*r1^3+2*r1^4)-3*a^4*r1^7*(480*M^4-679*M^3*r1+497*M^2*r1^2-227*M*r1^3+45*r1^4)+a^2*r1^8*(1524*M^5-2676*M^4*r1+2159*M^3*r1^2-1125*M^2*r1^3+378*M*r1^4-58*r1^5)+2*a^9*(-36*M^(3/2)*r1^(9/2)+5*Sqrt[M*r1^11])-2*a^7*(87*M^(5/2)*r1^(11/2)-200*M^(3/2)*r1^(13/2)+79*Sqrt[M*r1^15])-6*a^5*(-208*M^(7/2)*r1^(13/2)+413*M^(5/2)*r1^(15/2)-248*M^(3/2)*r1^(17/2)+45*Sqrt[M*r1^19])-2*a^3*(1020*M^(9/2)*r1^(15/2)-2312*M^(7/2)*r1^(17/2)+1821*M^(5/2)*r1^(19/2)-576*M^(3/2)*r1^(21/2)+58*Sqrt[M*r1^23])+2*a*(528*M^(11/2)*r1^(17/2)-1348*M^(9/2)*r1^(19/2)+1256*M^(7/2)*r1^(21/2)-501*M^(5/2)*r1^(23/2)+68*M^(3/2)*r1^(25/2)+2*Sqrt[M*r1^27]))*Δθ^4)/(48*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^6))+Δr^3*((-4*(84*a^18*M^4*(M-6*r1)*r1^5-84*a^19*(M*r1)^(9/2)+2*a^17*M^(7/2)*r1^(11/2)*(497*M^2+34*M*r1-657*r1^2)-a^16*M^3*r1^6*(987*M^3-6359*M^2*r1+1241*M*r1^2+2043*r1^3)+3*r1^20*(-2*M+r1)^4*(139*M^4-163*M^3*r1+78*M^2*r1^2-27*M*r1^3+5*r1^4)-2*a^15*M^(5/2)*r1^(13/2)*(2491*M^4+693*M^3*r1-8327*M^2*r1^2+2161*M*r1^3+1146*r1^4)+a^14*M^2*r1^7*(4953*M^5-34147*M^4*r1+12468*M^3*r1^2+22725*M^2*r1^3-6839*M*r1^4-2112*r1^5)+2*a^13*M^(3/2)*r1^(15/2)*(6768*M^6+5271*M^5*r1-46124*M^4*r1^2+23925*M^3*r1^3+8673*M^2*r1^4-3526*M*r1^5-783*r1^6)+3*a^2*(2*M-r1)^3*r1^17*(4170*M^6-8643*M^5*r1+6535*M^4*r1^2-2640*M^3*r1^3+739*M^2*r1^4-91*M*r1^5-10*r1^6)-a^12*M*r1^8*(13584*M^7-99948*M^6*r1+47247*M^5*r1^2+116665*M^4*r1^3-73593*M^3*r1^4-8418*M^2*r1^5+6176*M*r1^6+807*r1^7)+a^4*r1^14*(-2*M+r1)^2*(25020*M^8-86568*M^7*r1+47247*M^6*r1^2+52637*M^5*r1^3-59923*M^4*r1^4+22702*M^3*r1^5-5708*M^2*r1^6+1095*M*r1^7-30*r1^8)+a^10*r1^9*(21432*M^9-167920*M^8*r1+71758*M^7*r1^2+368622*M^6*r1^3-349549*M^5*r1^4+38841*M^4*r1^5+31848*M^3*r1^6+793*M^2*r1^7-2691*M*r1^8-30*r1^9)+a^8*r1^10*(-18384*M^10+153056*M^9*r1+5256*M^8*r1^2-749364*M^7*r1^3+895515*M^6*r1^4-283335*M^5*r1^5-39702*M^4*r1^6+9784*M^3*r1^7+12174*M^2*r1^8-2535*M*r1^9-105*r1^10)+a^6*r1^11*(6672*M^11-58896*M^10*r1-129384*M^9*r1^2+882512*M^8*r1^3-1177191*M^7*r1^4+498765*M^6*r1^5+69102*M^5*r1^6-94005*M^4*r1^7+12021*M^3*r1^8+1846*M^2*r1^9+270*M*r1^10-120*r1^11)-2*a^11*(20216*M^(15/2)*r1^(19/2)-143106*M^(13/2)*r1^(21/2)+108856*M^(11/2)*r1^(23/2)+24523*M^(9/2)*r1^(25/2)-30117*M^(7/2)*r1^(27/2)-1975*M^(5/2)*r1^(29/2)+2411*M^(3/2)*r1^(31/2)+10504*(M*r1)^(17/2)+120*Sqrt[M*r1^33])+2*a^9*(42072*M^(17/2)*r1^(21/2)-260632*M^(15/2)*r1^(23/2)+246862*M^(13/2)*r1^(25/2)+51225*M^(11/2)*r1^(27/2)-125749*M^(9/2)*r1^(29/2)+23833*M^(7/2)*r1^(31/2)+9117*M^(5/2)*r1^(33/2)-1172*M^(3/2)*r1^(35/2)+8816*(M*r1)^(19/2)-420*Sqrt[M*r1^37])-2*a^7*(45456*M^(19/2)*r1^(23/2)-261208*M^(17/2)*r1^(25/2)+257544*M^(15/2)*r1^(27/2)+159327*M^(13/2)*r1^(29/2)-348363*M^(11/2)*r1^(31/2)+166503*M^(9/2)*r1^(33/2)-23289*M^(7/2)*r1^(35/2)+1996*M^(5/2)*r1^(37/2)-2322*M^(3/2)*r1^(39/2)+3120*(M*r1)^(21/2)+480*Sqrt[M*r1^41])-2*a^5*(-20016*M^(21/2)*r1^(25/2)+111168*M^(19/2)*r1^(27/2)-51480*M^(17/2)*r1^(29/2)-338152*M^(15/2)*r1^(31/2)+576717*M^(13/2)*r1^(33/2)-390922*M^(11/2)*r1^(35/2)+135709*M^(9/2)*r1^(37/2)-31071*M^(7/2)*r1^(39/2)+7796*M^(5/2)*r1^(41/2)-1633*M^(3/2)*r1^(43/2)+120*Sqrt[M*r1^45])+2*a^3*(66720*M^(19/2)*r1^(31/2)-260784*M^(17/2)*r1^(33/2)+388128*M^(15/2)*r1^(35/2)-283672*M^(13/2)*r1^(37/2)+102354*M^(11/2)*r1^(39/2)-9995*M^(9/2)*r1^(41/2)-6829*M^(7/2)*r1^(43/2)+3855*M^(5/2)*r1^(45/2)-1031*M^(3/2)*r1^(47/2)+120*Sqrt[M*r1^49])+6*a*(6672*M^(17/2)*r1^(37/2)-22304*M^(15/2)*r1^(39/2)+32776*M^(13/2)*r1^(41/2)-28168*M^(11/2)*r1^(43/2)+15881*M^(9/2)*r1^(45/2)-6168*M^(7/2)*r1^(47/2)+1631*M^(5/2)*r1^(49/2)-266*M^(3/2)*r1^(51/2)+20*Sqrt[M*r1^53]))*ΔQ^6)/(3*r1^9*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^4*(a^2+r1*(-2*M+r1))^4)+((12*a^16*M^3*r1^4+12*a^15*M^(5/2)*r1^(9/2)*(14*M+9*r1)+6*a^14*M^2*r1^5*(-47*M^2+104*M*r1+57*r1^2)-2*a^13*M^(3/2)*r1^(11/2)*(893*M^3+358*M^2*r1-525*M*r1^2-264*r1^3)+3*(2*M-r1)^3*r1^16*(357*M^4-434*M^3*r1+230*M^2*r1^2-78*M*r1^3+13*r1^4)+3*a^12*M*r1^6*(753*M^4-2555*M^3*r1-193*M^2*r1^2+487*M*r1^3+144*r1^4)-12*a^2*r1^13*(-2*M+r1)^2*(-1071*M^6+2511*M^5*r1-1993*M^4*r1^2+800*M^3*r1^3-192*M^2*r1^4+7*M*r1^5+7*r1^6)+3*a^10*r1^7*(-2939*M^6+12542*M^5*r1-3910*M^4*r1^2-2834*M^3*r1^3-253*M^2*r1^4+556*M*r1^5+10*r1^6)+3*a^8*r1^8*(6122*M^7-30677*M^6*r1+17778*M^5*r1^2+8975*M^4*r1^3-4960*M^3*r1^4-1443*M^2*r1^5+504*M*r1^6+41*r1^7)+3*a^6*r1^9*(-6564*M^8+37324*M^7*r1-22957*M^6*r1^2-30962*M^5*r1^3+35284*M^4*r1^4-11426*M^3*r1^5+1559*M^2*r1^6-312*M*r1^7+50*r1^8)+3*a^4*r1^10*(2856*M^9-18052*M^8*r1-3046*M^7*r1^2+69525*M^6*r1^3-89633*M^5*r1^4+52665*M^4*r1^5-18029*M^3*r1^6+3998*M^2*r1^7-476*M*r1^8+4*r1^9)+2*a^11*(3819*M^(11/2)*r1^(13/2)+1353*M^(9/2)*r1^(15/2)-6047*M^(7/2)*r1^(17/2)-301*M^(5/2)*r1^(19/2)+960*M^(3/2)*r1^(21/2)+90*Sqrt[M*r1^23])+2*a^9*(-8202*M^(13/2)*r1^(15/2)-5883*M^(11/2)*r1^(17/2)+31503*M^(9/2)*r1^(19/2)-13281*M^(7/2)*r1^(21/2)-2006*M^(5/2)*r1^(23/2)+230*M^(3/2)*r1^(25/2)+369*Sqrt[M*r1^27])+2*a^7*(8836*M^(15/2)*r1^(17/2)+18716*M^(13/2)*r1^(19/2)-87681*M^(11/2)*r1^(21/2)+71101*M^(9/2)*r1^(23/2)-16843*M^(7/2)*r1^(25/2)+1971*M^(5/2)*r1^(27/2)-1800*M^(3/2)*r1^(29/2)+450*Sqrt[M*r1^31])+2*a^5*(-3816*M^(17/2)*r1^(19/2)-29292*M^(15/2)*r1^(21/2)+124402*M^(13/2)*r1^(23/2)-133885*M^(11/2)*r1^(25/2)+54048*M^(9/2)*r1^(27/2)-6989*M^(7/2)*r1^(29/2)+542*M^(5/2)*r1^(31/2)-384*M^(3/2)*r1^(33/2)+36*Sqrt[M*r1^35])-4*a^3*(-8568*M^(17/2)*r1^(23/2)+35076*M^(15/2)*r1^(25/2)-38742*M^(13/2)*r1^(27/2)+7603*M^(11/2)*r1^(29/2)+14129*M^(9/2)*r1^(31/2)-12471*M^(7/2)*r1^(33/2)+5044*M^(5/2)*r1^(35/2)-1168*M^(3/2)*r1^(37/2)+126*Sqrt[M*r1^39])-6*a*(-5712*M^(15/2)*r1^(29/2)+16904*M^(13/2)*r1^(31/2)-21900*M^(11/2)*r1^(33/2)+16458*M^(9/2)*r1^(35/2)-7924*M^(7/2)*r1^(37/2)+2475*M^(5/2)*r1^(39/2)-462*M^(3/2)*r1^(41/2)+39*Sqrt[M*r1^43]))*ΔQ^4*Δθ^2)/(3*r1^6*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3*(a^2+r1*(-2*M+r1))^4)+((54*a^13*M^(3/2)*r1^(7/2)+3*a^12*M*r1^4*(-11*M+45*r1)+a^10*r1^5*(117*M^3-927*M^2*r1+407*M*r1^2+27*r1^3)-r1^12*(-2*M+r1)^2*(732*M^4-1074*M^3*r1+677*M^2*r1^2-239*M*r1^3+38*r1^4)+a^8*r1^6*(438*M^4+1002*M^3*r1-1243*M^2*r1^2+65*M*r1^3+88*r1^4)+2*a^6*r1^7*(-1416*M^5+2883*M^4*r1-2007*M^3*r1^2+1023*M^2*r1^3-361*M*r1^4+38*r1^5)+a^4*r1^8*(4968*M^6-16296*M^5*r1+17714*M^4*r1^2-9972*M^3*r1^3+3141*M^2*r1^4-343*M*r1^5-42*r1^6)-a^2*r1^9*(2928*M^7-12024*M^6*r1+14512*M^5*r1^2-7418*M^4*r1^3+911*M^3*r1^4+991*M^2*r1^5-563*M*r1^6+95*r1^7)+2*a^11*(-153*M^(5/2)*r1^(9/2)+55*M^(3/2)*r1^(11/2)+54*Sqrt[M*r1^13])+2*a^9*(126*M^(7/2)*r1^(11/2)-95*M^(5/2)*r1^(13/2)-392*M^(3/2)*r1^(15/2)+176*Sqrt[M*r1^17])+4*a^7*(384*M^(9/2)*r1^(13/2)-246*M^(7/2)*r1^(15/2)+489*M^(5/2)*r1^(17/2)-383*M^(3/2)*r1^(19/2)+76*Sqrt[M*r1^21])-2*a^5*(1848*M^(11/2)*r1^(15/2)-640*M^(9/2)*r1^(17/2)-1008*M^(7/2)*r1^(19/2)+882*M^(5/2)*r1^(21/2)-391*M^(3/2)*r1^(23/2)+84*Sqrt[M*r1^25])+a^3*(2400*M^(13/2)*r1^(17/2)+4064*M^(11/2)*r1^(19/2)-15712*M^(9/2)*r1^(21/2)+17368*M^(7/2)*r1^(23/2)-9874*M^(5/2)*r1^(25/2)+2990*M^(3/2)*r1^(27/2)-380*Sqrt[M*r1^29])-2*a*(2928*M^(13/2)*r1^(21/2)-8424*M^(11/2)*r1^(23/2)+10672*M^(9/2)*r1^(25/2)-7634*M^(7/2)*r1^(27/2)+3231*M^(5/2)*r1^(29/2)-758*M^(3/2)*r1^(31/2)+76*Sqrt[M*r1^33]))*ΔQ^2*Δθ^4)/(12*r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^4)+((42*a^9*Sqrt[M*r1^7]+3*a^8*r1^4*(3*M+7*r1)+a^6*r1^5*(-69*M^2-96*M*r1+49*r1^2)+r1^8*(-2*M+r1)^2*(66*M^3-69*M^2*r1+43*M*r1^2-14*r1^3)+3*a^4*r1^6*(78*M^3+11*M^2*r1-40*M*r1^2+7*r1^3)-3*a^2*r1^7*(132*M^4-140*M^3*r1+65*M^2*r1^2-28*M*r1^3+7*r1^4)+a^7*(-270*M^(3/2)*r1^(9/2)+98*Sqrt[M*r1^11])+6*a^5*(98*M^(5/2)*r1^(11/2)-61*M^(3/2)*r1^(13/2)+7*Sqrt[M*r1^15])-6*a^3*(76*M^(7/2)*r1^(13/2)-40*M^(5/2)*r1^(15/2)-13*M^(3/2)*r1^(17/2)+7*Sqrt[M*r1^19])+a*(48*M^(9/2)*r1^(15/2)+200*M^(7/2)*r1^(17/2)-348*M^(5/2)*r1^(19/2)+174*M^(3/2)*r1^(21/2)-28*Sqrt[M*r1^23]))*Δθ^6)/(48*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1))^4))+Δr*((-16*M*(-24*a^21*M^(9/2)*r1^(7/2)+24*a^20*M^4*(M-8*r1)*r1^4+12*a*M^(3/2)*(29*M-15*r1)*(2*M-r1)^5*r1^(41/2)+4*a^19*M^(7/2)*r1^(9/2)*(71*M^2+13*M*r1-168*r1^2)+3*r1^22*(-2*M+r1)^4*(29*M^3-25*M^2*r1+3*M*r1^2+r1^3)-2*a^18*M^3*r1^5*(141*M^3-1204*M^2*r1+223*M*r1^2+672*r1^3)-2*a^17*M^(5/2)*r1^(11/2)*(701*M^4+435*M^3*r1-4347*M^2*r1^2+1279*M*r1^3+840*r1^4)+a^16*M^2*r1^6*(1383*M^5-12556*M^4*r1+3504*M^3*r1^2+16952*M^2*r1^3-6091*M*r1^4-1344*r1^5)+3*a^2*(2*M-r1)^3*r1^19*(1624*M^5-2770*M^4*r1+1533*M^3*r1^2-285*M^2*r1^3+15*M*r1^4-5*r1^5)+4*a^15*M^(3/2)*r1^(13/2)*(924*M^6+1392*M^5*r1-11806*M^4*r1^2+6255*M^3*r1^3+4472*M^2*r1^4-2077*M*r1^5-168*r1^6)+a^4*r1^16*(-2*M+r1)^2*(24360*M^7-67500*M^6*r1+44682*M^5*r1^2+9935*M^4*r1^3-18931*M^3*r1^4+5755*M^2*r1^5-515*M*r1^6+30*r1^7)-a^14*M*r1^7*(3624*M^7-34860*M^6*r1+7800*M^5*r1^2+93623*M^4*r1^3-62721*M^3*r1^4-6375*M^2*r1^5+6973*M*r1^6+192*r1^7)+a^12*M*r1^8*(5352*M^8-54376*M^7*r1-6470*M^6*r1^2+286824*M^5*r1^3-258970*M^4*r1^4-11221*M^3*r1^5+65289*M^2*r1^6-12311*M*r1^7-1013*r1^8)+a^10*r1^9*(-4224*M^10+45200*M^9*r1+52776*M^8*r1^2-507772*M^7*r1^3+524686*M^6*r1^4+61662*M^5*r1^5-282112*M^4*r1^6+108217*M^3*r1^7-4965*M^2*r1^8-2207*M*r1^9+3*r1^10)+a^6*r1^13*(38976*M^10-196080*M^9*r1+89040*M^8*r1^2+567112*M^7*r1^3-914652*M^6*r1^4+517345*M^5*r1^5-72607*M^4*r1^6-39219*M^3*r1^7+15769*M^2*r1^8-1682*M*r1^9+30*r1^10)+a^8*r1^10*(1392*M^11-15648*M^10*r1-78552*M^9*r1^2+487048*M^8*r1^3-486681*M^7*r1^4-299652*M^6*r1^5+693120*M^5*r1^6-357402*M^4*r1^7+47646*M^3*r1^8+10931*M^2*r1^9-2553*M*r1^10+15*r1^11)-2*a^13*(2744*M^(17/2)*r1^(15/2)+9040*M^(15/2)*r1^(17/2)-68802*M^(13/2)*r1^(19/2)+46982*M^(11/2)*r1^(21/2)+46757*M^(9/2)*r1^(23/2)-42645*M^(7/2)*r1^(25/2)+3961*M^(5/2)*r1^(27/2)+1783*M^(3/2)*r1^(29/2)+12*Sqrt[M*r1^31])-4*a^11*(-1088*M^(19/2)*r1^(17/2)-7992*M^(17/2)*r1^(19/2)+56628*M^(15/2)*r1^(21/2)-39582*M^(13/2)*r1^(23/2)-76629*M^(11/2)*r1^(25/2)+91887*M^(9/2)*r1^(27/2)-21783*M^(7/2)*r1^(29/2)-5526*M^(5/2)*r1^(31/2)+1872*M^(3/2)*r1^(33/2)+29*Sqrt[M*r1^35])-2*a^9*(720*M^(21/2)*r1^(19/2)+14736*M^(19/2)*r1^(21/2)-99736*M^(17/2)*r1^(23/2)+41136*M^(15/2)*r1^(25/2)+312293*M^(13/2)*r1^(27/2)-409325*M^(11/2)*r1^(29/2)+132135*M^(9/2)*r1^(31/2)+39905*M^(7/2)*r1^(33/2)-29216*M^(5/2)*r1^(35/2)+3792*M^(3/2)*r1^(37/2)+112*Sqrt[M*r1^39])-4*a^7*(-2784*M^(21/2)*r1^(23/2)+18336*M^(19/2)*r1^(25/2)+18624*M^(17/2)*r1^(27/2)-176080*M^(15/2)*r1^(29/2)+227586*M^(13/2)*r1^(31/2)-63670*M^(11/2)*r1^(33/2)-63185*M^(9/2)*r1^(35/2)+50934*M^(7/2)*r1^(37/2)-12685*M^(5/2)*r1^(39/2)+806*M^(3/2)*r1^(41/2)+54*Sqrt[M*r1^43])-2*a^5*(-38976*M^(19/2)*r1^(29/2)+165552*M^(17/2)*r1^(31/2)-174384*M^(15/2)*r1^(33/2)-66472*M^(13/2)*r1^(35/2)+244716*M^(11/2)*r1^(37/2)-180189*M^(9/2)*r1^(39/2)+57777*M^(7/2)*r1^(41/2)-6987*M^(5/2)*r1^(43/2)-165*M^(3/2)*r1^(45/2)+52*Sqrt[M*r1^47])-4*a^3*(-19488*M^(17/2)*r1^(35/2)+67152*M^(15/2)*r1^(37/2)-90672*M^(13/2)*r1^(39/2)+59848*M^(11/2)*r1^(41/2)-18186*M^(9/2)*r1^(43/2)+641*M^(7/2)*r1^(45/2)+970*M^(5/2)*r1^(47/2)-186*M^(3/2)*r1^(49/2)+5*Sqrt[M*r1^51]))*ΔQ^8)/(3*r1^11*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^5*(a^2+r1*(-2*M+r1))^2)-(4*(84*a^16*M^4*(M-6*r1)*r1^5-84*a^17*(M*r1)^(9/2)+2*a^15*M^(7/2)*r1^(11/2)*(413*M^2+40*M*r1-621*r1^2)-a^14*M^3*r1^6*(819*M^3-5375*M^2*r1+1313*M*r1^2+1575*r1^3)-3*(2*M-r1)^3*r1^19*(97*M^4-86*M^3*r1+27*M^2*r1^2-8*M*r1^3+2*r1^4)-2*a^13*M^(5/2)*r1^(13/2)*(1623*M^4+792*M^3*r1-6955*M^2*r1^2+2374*M*r1^3+498*r1^4)+a^12*M^2*r1^7*(3189*M^5-22734*M^4*r1+8751*M^3*r1^2+16724*M^2*r1^3-7082*M*r1^4-132*r1^5)+3*a^2*r1^16*(-2*M+r1)^2*(-2910*M^6+5529*M^5*r1-3770*M^4*r1^2+1344*M^3*r1^3-316*M^2*r1^4+23*M*r1^5+8*r1^6)+2*a^11*M^(3/2)*r1^(15/2)*(3186*M^6+4668*M^5*r1-31404*M^4*r1^2+19182*M^3*r1^3+2677*M^2*r1^4-2554*M*r1^5+117*r1^6)-a^10*M*r1^8*(6198*M^7-47715*M^6*r1+16437*M^5*r1^2+79593*M^4*r1^3-61104*M^3*r1^4+9391*M^2*r1^5+1169*M*r1^6-165*r1^7)+a^8*r1^9*(6012*M^9-49732*M^8*r1-5987*M^7*r1^2+202569*M^6*r1^3-200410*M^5*r1^4+55333*M^4*r1^5+5451*M^3*r1^6-4590*M^2*r1^7+648*M*r1^8+6*r1^9)+a^4*r1^13*(-34920*M^9+137340*M^8*r1-128466*M^7*r1^2-29707*M^6*r1^3+115621*M^5*r1^4-79836*M^4*r1^5+28535*M^3*r1^6-5795*M^2*r1^7+444*M*r1^8+36*r1^9)+a^6*r1^10*(-2328*M^10+20604*M^9*r1+46182*M^8*r1^2-264031*M^7*r1^3+286066*M^6*r1^4-82581*M^5*r1^5-33937*M^4*r1^6+28690*M^3*r1^7-7923*M^2*r1^8+894*M*r1^9+24*r1^10)+2*a^9*(-12194*M^(15/2)*r1^(19/2)+71058*M^(13/2)*r1^(21/2)-55576*M^(11/2)*r1^(23/2)-12215*M^(9/2)*r1^(25/2)+21936*M^(7/2)*r1^(27/2)-5857*M^(5/2)*r1^(29/2)+388*M^(3/2)*r1^(31/2)-3124*(M*r1)^(17/2)+24*Sqrt[M*r1^33])+2*a^7*(14904*M^(17/2)*r1^(21/2)-80258*M^(15/2)*r1^(23/2)+62168*M^(13/2)*r1^(25/2)+51831*M^(11/2)*r1^(27/2)-80708*M^(9/2)*r1^(29/2)+35267*M^(7/2)*r1^(31/2)-6324*M^(5/2)*r1^(33/2)+192*M^(3/2)*r1^(35/2)+1224*(M*r1)^(19/2)+96*Sqrt[M*r1^37])+2*a^5*(-6984*M^(19/2)*r1^(23/2)+36108*M^(17/2)*r1^(25/2)-5862*M^(15/2)*r1^(27/2)-106679*M^(13/2)*r1^(29/2)+140774*M^(11/2)*r1^(31/2)-75543*M^(9/2)*r1^(33/2)+19108*M^(7/2)*r1^(35/2)-1336*M^(5/2)*r1^(37/2)-582*M^(3/2)*r1^(39/2)+144*Sqrt[M*r1^41])+2*a^3*(-23280*M^(17/2)*r1^(29/2)+76800*M^(15/2)*r1^(31/2)-89796*M^(13/2)*r1^(33/2)+46016*M^(11/2)*r1^(35/2)-6938*M^(9/2)*r1^(37/2)-3867*M^(7/2)*r1^(39/2)+2654*M^(5/2)*r1^(41/2)-773*M^(3/2)*r1^(43/2)+96*Sqrt[M*r1^45])+6*a*(-2328*M^(15/2)*r1^(35/2)+6084*M^(13/2)*r1^(37/2)-6762*M^(11/2)*r1^(39/2)+4263*M^(9/2)*r1^(41/2)-1738*M^(7/2)*r1^(43/2)+489*M^(5/2)*r1^(45/2)-90*M^(3/2)*r1^(47/2)+8*Sqrt[M*r1^49]))*ΔQ^6*Δθ^2)/(3*r1^9*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^4*(a^2+r1*(-2*M+r1))^2)+((-6*a^14*M^3*r1^4+2*a^13*M^(5/2)*(51*M-19*r1)*r1^(9/2)-3*a^12*M^2*r1^5*(19*M^2-138*M*r1+33*r1^2)+2*a^11*M^(3/2)*r1^(11/2)*(-391*M^3+138*M^2*r1+281*M*r1^2-68*r1^3)+a^10*M*r1^6*(645*M^4-3603*M^3*r1+1833*M^2*r1^2+123*M*r1^3-104*r1^4)-r1^15*(-2*M+r1)^2*(312*M^4-351*M^3*r1+193*M^2*r1^2-73*M*r1^3+13*r1^4)-a^8*r1^7*(2016*M^6-11493*M^5*r1+7767*M^4*r1^2+1608*M^3*r1^3-2248*M^2*r1^4+473*M*r1^5+7*r1^6)+a^6*r1^8*(2628*M^7-15972*M^6*r1+10143*M^5*r1^2+10701*M^4*r1^3-13347*M^3*r1^4+5217*M^2*r1^5-706*M*r1^6-34*r1^7)-2*a^2*r1^12*(3744*M^7-11004*M^6*r1+12424*M^5*r1^2-7337*M^4*r1^3+2360*M^3*r1^4-242*M^2*r1^5-89*M*r1^6+23*r1^7)+a^4*r1^9*(-1248*M^8+8172*M^7*r1+1452*M^6*r1^2-27045*M^5*r1^3+31420*M^4*r1^4-16413*M^3*r1^5+4212*M^2*r1^6-284*M*r1^7-60*r1^8)+a^9*(2240*M^(11/2)*r1^(13/2)+6*M^(9/2)*r1^(15/2)-5596*M^(7/2)*r1^(17/2)+3262*M^(5/2)*r1^(19/2)-430*M^(3/2)*r1^(21/2)-42*Sqrt[M*r1^23])-2*a^7*(1420*M^(13/2)*r1^(15/2)+1688*M^(11/2)*r1^(17/2)-10301*M^(9/2)*r1^(19/2)+8582*M^(7/2)*r1^(21/2)-2331*M^(5/2)*r1^(23/2)-40*M^(3/2)*r1^(25/2)+102*Sqrt[M*r1^27])-2*a^5*(-672*M^(15/2)*r1^(17/2)-3812*M^(13/2)*r1^(19/2)+16472*M^(11/2)*r1^(21/2)-16257*M^(9/2)*r1^(23/2)+5507*M^(7/2)*r1^(25/2)+456*M^(5/2)*r1^(27/2)-834*M^(3/2)*r1^(29/2)+180*Sqrt[M*r1^31])-4*a^3*(1248*M^(15/2)*r1^(21/2)-4812*M^(13/2)*r1^(23/2)+4420*M^(11/2)*r1^(25/2)-135*M^(9/2)*r1^(27/2)-2110*M^(7/2)*r1^(29/2)+1550*M^(5/2)*r1^(31/2)-514*M^(3/2)*r1^(33/2)+69*Sqrt[M*r1^35])-6*a*(832*M^(13/2)*r1^(27/2)-2040*M^(11/2)*r1^(29/2)+2200*M^(9/2)*r1^(31/2)-1386*M^(7/2)*r1^(33/2)+548*M^(5/2)*r1^(35/2)-127*M^(3/2)*r1^(37/2)+13*Sqrt[M*r1^39]))*ΔQ^4*Δθ^4)/(3*r1^6*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^3*(a^2+r1*(-2*M+r1))^2)+((18*a^11*M^(3/2)*r1^(7/2)-3*a^10*M*(M-15*r1)*r1^4+r1^11*(-2*M+r1)^2*(54*M^3-51*M^2*r1+31*M*r1^2-8*r1^3)+a^8*r1^5*(-27*M^3-216*M^2*r1+92*M*r1^2+9*r1^3)+a^6*r1^6*(198*M^4+159*M^3*r1-207*M^2*r1^2-21*M*r1^3+19*r1^4)+3*a^4*r1^7*(-124*M^5+148*M^4*r1-61*M^3*r1^2+57*M^2*r1^3-25*M*r1^4+r1^5)+a^2*r1^8*(216*M^6-516*M^5*r1+314*M^4*r1^2-75*M^3*r1^3-42*M^2*r1^4+56*M*r1^5-15*r1^6)+a^9*(-90*M^(5/2)*r1^(9/2)+32*M^(3/2)*r1^(11/2)+36*Sqrt[M*r1^13])+4*a^7*(33*M^(7/2)*r1^(11/2)-36*M^(5/2)*r1^(13/2)-39*M^(3/2)*r1^(15/2)+19*Sqrt[M*r1^17])+12*a^5*(-2*M^(9/2)*r1^(13/2)+29*M^(7/2)*r1^(15/2)+M^(5/2)*r1^(17/2)-10*M^(3/2)*r1^(19/2)+Sqrt[M*r1^21])-2*a^3*(24*M^(11/2)*r1^(15/2)+296*M^(9/2)*r1^(17/2)-390*M^(7/2)*r1^(19/2)+264*M^(5/2)*r1^(21/2)-133*M^(3/2)*r1^(23/2)+30*Sqrt[M*r1^25])+a*(432*M^(11/2)*r1^(19/2)-888*M^(9/2)*r1^(21/2)+916*M^(7/2)*r1^(23/2)-594*M^(5/2)*r1^(25/2)+216*M^(3/2)*r1^(27/2)-32*Sqrt[M*r1^29]))*ΔQ^2*Δθ^6)/(12*r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])^2*(a^2+r1*(-2*M+r1))^2)-(r1*(-18*a^5*Sqrt[M*r1^5]-3*a^4*r1^3*(M+3*r1)+2*a^2*r1^4*(3*M^2+9*M*r1-4*r1^2)+r1^6*(-6*M^2+M*r1+r1^2)+a^3*(60*M^(3/2)*r1^(7/2)-16*Sqrt[M*r1^9])+2*a*(-24*M^(5/2)*r1^(9/2)+10*M^(3/2)*r1^(11/2)+Sqrt[M*r1^13]))*Δθ^8)/(48*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])*(a^2+r1*(-2*M+r1)))))/(4*(r1^2+(a^2*(2*M+r1))/r1+(M*(a^2*r1+r1^3-2*a*Sqrt[M*r1^3])^2)/(r1^3*(-3*M*r1+r1^2+2*a*Sqrt[M*r1])))*ΔQ^2+(r1^2*Δr^2)/(a^2+r1*(-2*M+r1))+r1^2*Δθ^2)^(7/2);

Circular geodesic (alternate form)

This alternate form was used in: “Self force via m-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime”, Dolan, Barack and Wardell (2011). These expressions were given in the appendix there; we given them here for convenience.

Note that the following expressions use the a-dimensionalized variables:

(OverTilde[a])=a/M
(Subscript[(OverTilde[r]), 0])=r1/M
(Subscript[(OverTilde[Δ]), 0])=Δ/(M^2)=((a^2)+r1(r1-2M))/(M^2)
((OverTilde[u])^ϕ)=uϕ1/M

The term (Subscript[α, (5)]) is

α5=-(1/(6 (Subscript[(OverTilde[r]), 0]^6) (Subscript[(OverTilde[Δ]), 0]^4)))(M^(3/2)) ((uϕ)^2) ((Subscript[(OverTilde[r]), 0]^4) (Subscript[(OverTilde[Δ]), 0]) ((δr)^2)+(((OverTilde[a])^2)-(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]^3) ((δr)^3)+(Subscript[(OverTilde[r]), 0]^4) (Subscript[(OverTilde[Δ]), 0]^2) ((δθ)^2)+(Subscript[(OverTilde[r]), 0]) ((Subscript[(OverTilde[r]), 0]^3)+((OverTilde[a])^2) (2+(Subscript[(OverTilde[r]), 0]))) (Subscript[(OverTilde[Δ]), 0]^2) ((δϕ)^2)+δr ((Subscript[(OverTilde[r]), 0]^3) (Subscript[(OverTilde[Δ]), 0]^2) ((δθ)^2)+(-((OverTilde[a])^2)+(Subscript[(OverTilde[r]), 0]^3)) (Subscript[(OverTilde[Δ]), 0]^2) ((δϕ)^2))) ((Subscript[(OverTilde[r]), 0]^4) (-3 ((OverTilde[a])^2) (Sqrt[M])+(Sqrt[M]) (3-2 (Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0])+2 (OverTilde[a]) (Sqrt[M (Subscript[(OverTilde[r]), 0])])) (Subscript[(OverTilde[Δ]), 0]) ((δr)^2)-(((OverTilde[a])^2)-(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]^3) (3 ((OverTilde[a])^2) (Sqrt[M])-2 (OverTilde[a]) (Sqrt[M (Subscript[(OverTilde[r]), 0])])+(Sqrt[M]) (Subscript[(OverTilde[r]), 0]) (-3+2 (Subscript[(OverTilde[r]), 0]))) ((δr)^3)+(Subscript[(OverTilde[r]), 0]^4) (3 ((OverTilde[a])^2) (Sqrt[M])+(Sqrt[M]) (Subscript[(OverTilde[r]), 0]^2)-4 (OverTilde[a]) (Sqrt[M (Subscript[(OverTilde[r]), 0])])) (Subscript[(OverTilde[Δ]), 0]^2) ((δθ)^2)+(Subscript[(OverTilde[r]), 0]) (((OverTilde[a])^2) (Sqrt[M])+(Sqrt[M]) (Subscript[(OverTilde[r]), 0]^3)+2 (OverTilde[a]) (Subscript[(OverTilde[r]), 0]) (Sqrt[M (Subscript[(OverTilde[r]), 0])])) (Subscript[(OverTilde[Δ]), 0]^3) ((δϕ)^2)+δr ((Subscript[(OverTilde[r]), 0]^3) (9 ((OverTilde[a])^2) (Sqrt[M])-10 (OverTilde[a]) (Sqrt[M (Subscript[(OverTilde[r]), 0])])+(Sqrt[M]) (Subscript[(OverTilde[r]), 0]) (-3+4 (Subscript[(OverTilde[r]), 0]))) (Subscript[(OverTilde[Δ]), 0]^2) ((δθ)^2)+(-3 ((OverTilde[a])^4) (Sqrt[M])+2 (OverTilde[a]) (-1+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]^2) (Sqrt[M (Subscript[(OverTilde[r]), 0])])+(Sqrt[M]) (Subscript[(OverTilde[r]), 0]^4) (-7+4 (Subscript[(OverTilde[r]), 0]))+((OverTilde[a])^2) (Sqrt[M]) (Subscript[(OverTilde[r]), 0]) (5-2 (Subscript[(OverTilde[r]), 0])+3 (Subscript[(OverTilde[r]), 0]^2))) (Subscript[(OverTilde[Δ]), 0]^2) ((δϕ)^2)));

The term (Subscript[β, (5)]) is given by

β5=(1/(4 (Subscript[(OverTilde[r]), 0]^7)))(M^3) ut uϕ (-ut+(OverTilde[a]) M uϕ) (-2 (OverTilde[a]) ut+M (Subscript[(OverTilde[r]), 0]^3) uϕ+((OverTilde[a])^2) M (2+(Subscript[(OverTilde[r]), 0])) uϕ) δr ((δϕ)^2) (3 (Subscript[(OverTilde[r]), 0]^4) ((δr)^2)+3 (Subscript[(OverTilde[r]), 0]^4) (Subscript[(OverTilde[Δ]), 0]) ((δθ)^2)+(6 ((OverTilde[a])^2) (Subscript[(OverTilde[r]), 0])+3 ((OverTilde[a])^2) (Subscript[(OverTilde[r]), 0]^2)+3 (Subscript[(OverTilde[r]), 0]^4)+8 ((OverTilde[a])^2) (ut^2)-8 (OverTilde[a]) M ((Subscript[(OverTilde[r]), 0]^3)+((OverTilde[a])^2) (2+(Subscript[(OverTilde[r]), 0]))) ut uϕ+2 (M^2) ((((Subscript[(OverTilde[r]), 0]^3)+((OverTilde[a])^2) (2+(Subscript[(OverTilde[r]), 0]))))^2) ((uϕ)^2)) (Subscript[(OverTilde[Δ]), 0]) ((δϕ)^2))-(1/(8 (Subscript[(OverTilde[r]), 0]^5) (Subscript[(OverTilde[Δ]), 0]^2)))(M^2) δr ((Subscript[(OverTilde[r]), 0]^3) ((δr)^2)+(Subscript[(OverTilde[r]), 0]^3) (Subscript[(OverTilde[Δ]), 0]) ((δθ)^2)+((Subscript[(OverTilde[r]), 0]^3)+((OverTilde[a])^2) (2+(Subscript[(OverTilde[r]), 0]))) (Subscript[(OverTilde[Δ]), 0]) ((δϕ)^2)) ((-10 ((OverTilde[a])^3) M ut uϕ-8 (OverTilde[a]) M (-1+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]) ut uϕ+5 ((OverTilde[a])^4) (M^2) ((uϕ)^2)+(Subscript[(OverTilde[r]), 0]) (2 (-2+(Subscript[(OverTilde[r]), 0])) (ut^2)+(M^2) (Subscript[(OverTilde[r]), 0]^3) ((uϕ)^2))+((OverTilde[a])^2) (5 (ut^2)+2 (M^2) (Subscript[(OverTilde[r]), 0]) (-2+3 (Subscript[(OverTilde[r]), 0])) ((uϕ)^2))) ((δr)^2)+(30 ((OverTilde[a])^3) M ut uϕ+2 (OverTilde[a]) M (Subscript[(OverTilde[r]), 0]) (-6+11 (Subscript[(OverTilde[r]), 0])) ut uϕ-15 ((OverTilde[a])^4) (M^2) ((uϕ)^2)+((OverTilde[a])^2) (-15 (ut^2)+(M^2) (6-19 (Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]) ((uϕ)^2))+(Subscript[(OverTilde[r]), 0]) (-3 (-2+(Subscript[(OverTilde[r]), 0])) (ut^2)-4 (M^2) (Subscript[(OverTilde[r]), 0]^3) ((uϕ)^2))) (Subscript[(OverTilde[Δ]), 0]) ((δθ)^2)+ut (-3 ut+2 (OverTilde[a]) M uϕ) (Subscript[(OverTilde[Δ]), 0]^2) ((δϕ)^2));

The coefficients of the denominator are given by:

{(Subscript[𝒮, 5,0,0])==((((OverTilde[a])^4) (4-9 (Subscript[(OverTilde[r]), 0]))+(Subscript[(OverTilde[r]), 0]^2) (-1+2 (Subscript[(OverTilde[r]), 0])-6 (Subscript[(OverTilde[r]), 0]^2))+((OverTilde[a])^2) (Subscript[(OverTilde[r]), 0]) (3+(Subscript[(OverTilde[r]), 0]) (-5+12 (Subscript[(OverTilde[r]), 0]))))/(12 (Subscript[(OverTilde[Δ]), 0]^4))),(Subscript[𝒮, 4,0,0])==((3 ((OverTilde[a])^4)+2 ((OverTilde[a])^2) (1-6 (Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0])+(Subscript[(OverTilde[r]), 0]^2) (-1+8 (Subscript[(OverTilde[r]), 0])))/(12 (Subscript[(OverTilde[Δ]), 0]^3))),(Subscript[𝒮, 3,2,0])==((((OverTilde[a])^2) (5-6 (Subscript[(OverTilde[r]), 0]))+(Subscript[(OverTilde[r]), 0]^2))/(12 (Subscript[(OverTilde[Δ]), 0]^2))),(Subscript[𝒮, 3,0,2])==(1/(12 (Subscript[(OverTilde[r]), 0]^2) (Subscript[(OverTilde[Δ]), 0]^2)))(((((OverTilde[u])^ϕ)))^2) ((-1+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]^6)+2 ((OverTilde[a])^5) (Sqrt[(Subscript[(OverTilde[r]), 0])]) (4+(Subscript[(OverTilde[r]), 0]))-((OverTilde[a])^6) (7+3 (Subscript[(OverTilde[r]), 0]))+((OverTilde[a])^4) ((Subscript[(OverTilde[r]), 0]) (26+(Subscript[(OverTilde[r]), 0])-23 (Subscript[(OverTilde[r]), 0]^2))-12 (Subscript[(OverTilde[Δ]), 0]))-4 (Subscript[(OverTilde[r]), 0]^4) (Subscript[(OverTilde[Δ]), 0])+4 ((OverTilde[a])^3) (Sqrt[(Subscript[(OverTilde[r]), 0])]) (-8 (Subscript[(OverTilde[r]), 0])+10 (Subscript[(OverTilde[r]), 0]^3)-3 (Subscript[(OverTilde[r]), 0]^4)+2 (Subscript[(OverTilde[Δ]), 0]))+2 (OverTilde[a]) (Subscript[(OverTilde[r]), 0]^(5/2)) ((Subscript[(OverTilde[r]), 0]) (6+(Subscript[(OverTilde[r]), 0]) (-22+13 (Subscript[(OverTilde[r]), 0]))-12 (Subscript[(OverTilde[Δ]), 0]))+8 (Subscript[(OverTilde[Δ]), 0]))+((OverTilde[a])^2) (Subscript[(OverTilde[r]), 0]) ((Subscript[(OverTilde[r]), 0]) (-6+(Subscript[(OverTilde[r]), 0]) (6+(Subscript[(OverTilde[r]), 0]) (19-(Subscript[(OverTilde[r]), 0]) (7+6 (Subscript[(OverTilde[r]), 0])))))+4 (5+(Subscript[(OverTilde[r]), 0]) (-4+3 (Subscript[(OverTilde[r]), 0]))) (Subscript[(OverTilde[Δ]), 0]))),(Subscript[𝒮, 3,0,0])==(((((OverTilde[a])^2)-(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]))/(Subscript[(OverTilde[Δ]), 0]^2)),(Subscript[𝒮, 2,2,0])==-((-3 ((OverTilde[a])^2)+(Subscript[(OverTilde[r]), 0]))/(6 (Subscript[(OverTilde[Δ]), 0]))),(Subscript[𝒮, 2,0,2])==(1/(6 (Subscript[(OverTilde[r]), 0]) (Subscript[(OverTilde[Δ]), 0])))(((((OverTilde[u])^ϕ)))^2) (((OverTilde[a])^4) (7+9 (Subscript[(OverTilde[r]), 0]))+2 ((OverTilde[a])^3) (Sqrt[(Subscript[(OverTilde[r]), 0])]) (-4+(Subscript[(OverTilde[r]), 0]) (-7+3 (Subscript[(OverTilde[r]), 0])))+2 (OverTilde[a]) (Subscript[(OverTilde[r]), 0]^(3/2)) (-7 (-1+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0])+6 (Subscript[(OverTilde[Δ]), 0]))+(Subscript[(OverTilde[r]), 0]^3) ((Subscript[(OverTilde[r]), 0])-(Subscript[(OverTilde[r]), 0]^2)+6 (Subscript[(OverTilde[Δ]), 0]))+((OverTilde[a])^2) ((-1+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]) (1+(Subscript[(OverTilde[r]), 0])) (5+3 (Subscript[(OverTilde[r]), 0]))+6 (Subscript[(OverTilde[Δ]), 0]))),(Subscript[𝒮, 2,0,0])==((Subscript[(OverTilde[r]), 0]^2)/(Subscript[(OverTilde[Δ]), 0])),(Subscript[𝒮, 1,4,0])==(1/12) (1-(Subscript[(OverTilde[r]), 0])),(Subscript[𝒮, 1,2,2])==(1/(12 (Subscript[(OverTilde[r]), 0]^2)))(2 (OverTilde[a]) (11-6 (Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]^(7/2))-2 ((OverTilde[a])^3) (Sqrt[(Subscript[(OverTilde[r]), 0])]) (16+5 (Subscript[(OverTilde[r]), 0]))+((OverTilde[a])^4) (29+9 (Subscript[(OverTilde[r]), 0]))+((OverTilde[a])^2) (Subscript[(OverTilde[r]), 0]) (12+(3-17 (Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]))-2 (Subscript[(OverTilde[r]), 0]^4) (-3+(Subscript[(OverTilde[r]), 0]) (2+3 (Subscript[(OverTilde[r]), 0])))) (((((OverTilde[u])^ϕ)))^2),(Subscript[𝒮, 1,2,0])==(Subscript[(OverTilde[r]), 0]),(Subscript[𝒮, 1,0,4])==-(1/(12 (Subscript[(OverTilde[r]), 0]^(11/2))))((OverTilde[a])+(Subscript[(OverTilde[r]), 0]^(3/2))) (6 ((OverTilde[a])^6)-((OverTilde[a])^5) (Sqrt[(Subscript[(OverTilde[r]), 0])]) (19+3 (Subscript[(OverTilde[r]), 0]))-((OverTilde[a])^3) (Subscript[(OverTilde[r]), 0]^(3/2)) (3+(Subscript[(OverTilde[r]), 0])) (-11+6 (Subscript[(OverTilde[r]), 0]))+(OverTilde[a]) (Subscript[(OverTilde[r]), 0]^(9/2)) (9+(-8+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]))+(Subscript[(OverTilde[r]), 0]^6) (-9+(Subscript[(OverTilde[r]), 0]) (4+(Subscript[(OverTilde[r]), 0])))+((OverTilde[a])^4) (Subscript[(OverTilde[r]), 0]) (-10+3 (Subscript[(OverTilde[r]), 0]) (5+(Subscript[(OverTilde[r]), 0])))+((OverTilde[a])^2) (Subscript[(OverTilde[r]), 0]^3) (-21+(Subscript[(OverTilde[r]), 0]) (3+8 (Subscript[(OverTilde[r]), 0])))) (((((OverTilde[u])^ϕ)))^2),(Subscript[𝒮, 1,0,2])==(-1+(Subscript[(OverTilde[r]), 0])) ((((OverTilde[a])+(Subscript[(OverTilde[r]), 0]^(3/2))))^2) (((((OverTilde[u])^ϕ)))^2),(Subscript[𝒮, 0,4,0])==(1/12) (3 ((OverTilde[a])^2)-(-2+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0])),(Subscript[𝒮, 0,2,2])==-(1/(6 (Subscript[(OverTilde[r]), 0])))(2 ((OverTilde[a])^3) (Sqrt[(Subscript[(OverTilde[r]), 0])]) (1+(Subscript[(OverTilde[r]), 0])) (-8+3 (Subscript[(OverTilde[r]), 0]))+(-1+(Subscript[(OverTilde[r]), 0])) (Subscript[(OverTilde[r]), 0]^4) (-2+3 (Subscript[(OverTilde[r]), 0]))+((OverTilde[a])^4) (11+9 (Subscript[(OverTilde[r]), 0]))+2 (OverTilde[a]) (Subscript[(OverTilde[r]), 0]^(5/2)) (2+(Subscript[(OverTilde[r]), 0]) (-11+3 (Subscript[(OverTilde[r]), 0])))+((OverTilde[a])^2) (Subscript[(OverTilde[r]), 0]) (2+(Subscript[(OverTilde[r]), 0]) (-3+(Subscript[(OverTilde[r]), 0]) (10+3 (Subscript[(OverTilde[r]), 0]))))) (((((OverTilde[u])^ϕ)))^2),(Subscript[𝒮, 0,2,0])==(Subscript[(OverTilde[r]), 0]^2),(Subscript[𝒮, 0,0,4])==((((OverTilde[a])-(Subscript[(OverTilde[r]), 0]^(3/2))) ((((OverTilde[a])+(Subscript[(OverTilde[r]), 0]^(3/2))))^2) (2 ((OverTilde[a])^2)+(OverTilde[a]) (-5+(Subscript[(OverTilde[r]), 0])) (Sqrt[(Subscript[(OverTilde[r]), 0])])+(Subscript[(OverTilde[r]), 0]^2) (1+(Subscript[(OverTilde[r]), 0]))) (((((OverTilde[u])^ϕ)))^2) (Subscript[(OverTilde[Δ]), 0]))/(12 (Subscript[(OverTilde[r]), 0]^(9/2)))),(Subscript[𝒮, 0,0,2])==((((OverTilde[a])+(Subscript[(OverTilde[r]), 0]^(3/2))))^2) (((((OverTilde[u])^ϕ)))^2) (Subscript[(OverTilde[Δ]), 0])}