Link(s):

Paper and ancilary files.

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

Author(s):

Donato Bini, Thibault Damour, Andrea Geralico, Stefano Laporta, Pierpaolo Mastrolia

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.