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arXiv · 1706.06877

Gravitational scattering of two black holes at the fourth post-Newtonian approximation

Donato Bini·Thibault Damour
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Abstract

We compute the (center-of-mass frame) scattering angle $\chi$ of hyperboliclike encounters of two spinning black holes, at the fourth post-Newtonian approximation level for orbital effects, and at the next-to-next-to-leading order for spin-dependent effects. We find it convenient to compute the gauge-invariant scattering angle (expressed as a function of energy, orbital angular momentum and spins) by using the Effective-One-Body formalism. The contribution to scattering associated with nonlocal, tail effects is computed by generalizing to the case of unbound motions the method of time-localization of the action introduced in the case of (small-eccentricity) bound motions by Damour, Jaranowski and Sch\"afer [Phys.\ Rev.\ D {\bf 91}, no. 8, 084024 (2015)].

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Donato Bini, Thibault Damour. 2017-06-21. Gravitational scattering of two black holes at the fourth post-Newtonian approximation. https://doi.org/10.1103/physrevd.96.064021

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