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

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.

preprint2013arXivOpen access
Donato BiniThibault Damour
gr-qc
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Donato BiniThibault Damour

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