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arXiv · 2008.09389

Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics

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

A recently introduced approach to the gravitational dynamics of binary systems involves intricate integrals, linked to nonlocal-in-time interactions arising at the 5-loop level of classical gravitational scattering. We complete the analytical evaluation of classical gravitational scattering at the sixth order in Newton's constant, $G$, and at the sixth post-Newtonian accuracy. We use computing techniques developed for the evaluation of multi-loop Feynman integrals to obtain our results in two ways: high-precision arithmetic, yielding reconstructed analytic expressions, and direct integration {\it via} Harmonic Polylogarithms. The analytic expression of the tail contribution to the scattering involve transcendental constants up to weight four.

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Donato Bini, Thibault Damour, Andrea Geralico, Stefano Laporta, Pierpaolo Mastrolia. 2020-08-21. Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics. https://arxiv.org/abs/2008.09389

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