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arXiv · 1907.11080

New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: redshift invariant

Donato Bini·Andrea Geralico
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Abstract

The Detweiler-Barack-Sago redshift function for particles moving along slightly eccentric equatorial orbits around a Kerr black hole is currently known up to the second order in eccentricity, second order in spin parameter, and the 8.5 post-Newtonian order. We improve the analytical computation of such a gauge-invariant quantity by including terms up to the fourth order in eccentricity at the same post-Newtonian approximation level. We also check that our results agrees with the corresponding post-Newtonian expectation of the same quantity, calculated by using the currently known Hamiltonian for spinning binaries.

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Donato Bini, Andrea Geralico. 2019-07-23. New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: redshift invariant. https://doi.org/10.1103/physrevd.100.104002

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