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arXiv · 2012.12918

Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy

Donato Bini·Thibault Damour·Andrea Geralico·Stefano Laporta·Pierpaolo Mastrolia
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Abstract

A recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated $\frac1r$-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multi-loop Feynman integrals (notably Harmonic Polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton's constant, $G$ (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).

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Donato Bini, Thibault Damour, Andrea Geralico, Stefano Laporta, Pierpaolo Mastrolia. 2020-12-23. Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy. https://doi.org/10.1103/physrevd.103.044038

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