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arXiv · 1503.02334

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

Chris Kavanagh·Adrian C. Ottewill·Barry Wardell
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Abstract

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, $ν$.

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Chris Kavanagh, Adrian C. Ottewill, Barry Wardell. 2021-05-05. Analytical high-order post-Newtonian expansions for extreme mass ratio binaries. https://doi.org/10.1103/physrevd.92.084025

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