Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
General Relativity and Quantum Cosmology
2015-06-16 v1
Abstract
We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing the gravitational interaction of two bodies within the effective one-body formalism. The (non logarithmic) coefficient a_5 (nu) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio nu. Its nu-independent part a_5 (0) is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation. Its nu-linear part a_5 (nu) - a_5 (0) is deduced from recent results of Jaranowski and Sch\"afer, and is found to be significantly negative.
Keywords
Cite
@article{arxiv.1305.4884,
title = {Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation},
author = {Donato Bini and Thibault Damour},
journal= {arXiv preprint arXiv:1305.4884},
year = {2015}
}
Comments
6 pages, no figures