# Post-Newtonian expansions for extreme mass ratio binaries

“Analytical high-order post-Newtonian expansions for extreme mass ratio binaries”,
Chris Kavanagh, Adrian Ottewill and Barry Wardell, arXiv:1503.02334.

“Analytical high-order post-Newtonian expansions for spinning extreme mass ratio binaries”,
Chris Kavanagh, Adrian Ottewill and Barry Wardell, arXiv:1601.03394.

In those papers, we derived high-order post-Newtonian expansions of the liner-in-mass-ratio corrections to gauge invariant quantites on the worldline of a point mass in a circular orbit around Schwarzschild and Kerr black holes. In the papers, due to space constraints we only gave the leading order terms in the expansion. We provide here all terms we have computed, including those which were omitted from the papers. If you find these expansions useful in your work, please cite the above papers.

The following expressions are available:

• PN-Invariants.nb: Mathematica notebook containing expressions for the gauge invariants $\Delta U$, $\Delta \psi$, $\Delta \lambda_1$, $\Delta \lambda_2$, $\Delta \lambda_3$ and $\Delta \lambda^B$.  These are alternately know to as the redshift invariant, spin-precession invariant and tidal invariants.
• PN-Invariants-Kerr.nb: Mathematica notebook containing expressions for Detweiler’s redshift invariant $\Delta U$ for circular orbits in Kerr spacetime.