Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation

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 Schäfer, and is found to be significantly negative.

6 pages, no figures

References in corpus (2)

• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry

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