Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.09389
- arXiv:
- arXiv:2008.09389
- Bibcode:
- 2020arXiv200809389B
- Keywords:
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- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 9 pages, no figures, one ancillary text file