Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations

The preprint of my latest paper with Niels Warburton is now available on the arXiv. The abstract for the article is below:

With a view to developing a formalism that will be applicable at second perturbative order, we devise a new practical scheme for computing the gravitational self-force experienced by a point mass moving in a curved background spacetime. Our method works in the frequency domain and employs the effective-source approach, in which a distributional source for the retarded metric perturbation is replaced with an effective source for a certain regularized self-field. A key ingredient of the calculation is the analytic determination of an appropriate puncture field from which the effective source and regularized residual field can be calculated. In addition to its application in our effective-source method, we also show how this puncture field can be used to derive tensor-harmonic mode-sum regularization parameters that improve the efficiency of the traditional mode-sum procedure. To demonstrate the method, we calculate the first-order-in-the-mass-ratio self-force and redshift invariant for a point mass on a circular orbit in Schwarzschild spacetime.

Update: The paper has now been published as  Phys. Rev. D92, 084019 (2015).

Octupolar invariants for compact binaries on quasi-circular orbits

The preprint of my latest paper with Patrick Nolan, Chris Kavanagh, Sam R Dolan, Adrian C Ottewill, and Niels Warburton is now available on the arXiv. The abstract for the article is below:

We extend the gravitational self-force methodology to identify and compute new $O(\mu)$ tidal invariants for a compact body of mass $\mu$ on a quasi-circular orbit about a black hole of mass $M \gg \mu$. In the octupolar sector we find seven new degrees of freedom, made up of 3+3 conservative/dissipative electric’ invariants and 3+1 magnetic’ invariants, satisfying 1+1 and 1+0 trace conditions. After formulating for equatorial circular orbits on Kerr spacetime, we calculate explicitly for Schwarzschild spacetime. We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the functional series method of Mano, Suzuki and Takasugi. We present (i) highly-accurate numerical data and (ii) high-order analytical post-Newtonian expansions. We demonstrate consistency between numerical and analytic results, and prior work. We explore the application of these invariants in effective one-body models, and binary black hole initial-data formulations, and conclude with a discussion of future work.

Update: The paper has now been published as Phys. Rev. D 92, 123008 (2015).

Talk at Perimeter Institute

On Tuesday, March 24 2015 I gave a talk at Perimeter Institute in Waterloo, Canada. In the presentation, I described xAct, a tensor algebra package for Mathematica which was primarily developed by Jose Maria Martin-Garcia. The talk is available online through the Perimeter Institute video library and the Mathematica notebook containing the slides from the talk are available for download separately.

Talk in UCD CASL seminar series

On Thursday, March 19 2015 I gave a talk in the CASL Seminar Series at University College Dublin. In the presentation, I gave an overview of my research on “Numerical Simulations of Black Hole Binaries”. The talk is available online in the above YouTube video.

Analytical high-order post-Newtonian expansions for extreme mass ratio binaries

The preprint of my latest paper with Chris Kavanagh and Adrian Ottewill is now available on the arXiv. The abstract for the article is below:

We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of  $\ell$, and in doing so develop an efficient new method for generating the MST renormalised angular momentum,  $\nu$.

Update: The paper has now been published as Phys. Rev. D 92, 084025 (2015).

Self-force: Computational Strategies

I have recently finished a review paper which is due to be published by Springer in Fundamental Theories of Physics Vol. 179, as part of the book Equations of Motion in Relativistic Gravity. A preprint of the article is available on the arXiv. The abstract for the article is below:

Building on substantial foundational progress in understanding the effect of a small body’s self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) mode-sum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.

Installing GRTensor on Mac OSX

GRTensor is a very handy Maple package for doing calculations in General Relativity. Given a specific metric, it’s great at calculating the components of tensors. You can define your own tensors or use the predefined ones. You can even define your own metrics.

The install instructions in the Readme file are fairly good if you’re a Windows or Linux user. As is often the case, however, there are one or two catches when installing on Mac OS X. With that in mind, the following instructions should help with the installation:

GRTensor: Metrics and Mac OS X

GRTensor is a very handy Maple package for doing calculations in General Relativity. Given a specific metric, it’s great at calculating the components of tensors. You can define your own tensors or use the predefined ones. You can even define your own metrics.

Unfortunately, getting it working on Mac OS X is a bit of a pain. This is due to a bug in GRTensor that has gone unfixed for quite a while. Fortunately, there is a straightforwarde solution.