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arXiv · 1601.02988

New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole

Donato Bini·Thibault Damour·Andrea Geralico
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Abstract

We raise the analytical knowledge of the eccentricity-expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the $e^2$ and $e^4$ contributions, and up to the 4th post-Newtonian order for the higher eccentricity contributions through $e^{20}$. We convert this information into an analytical knowledge of the effective-one-body radial potentials $\bar d(u)$, $ρ(u)$ and $q(u)$ through the 9.5th post-Newtonian order. We find that our analytical results are compatible with current corresponding numerical self-force data.

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Donato Bini, Thibault Damour, Andrea Geralico. 2016-05-03. New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole. https://doi.org/10.1103/physrevd.93.104017

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