Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory

Author:

Long Oliver1ORCID,Whittall Christopher2ORCID,Barack Leor2ORCID

Affiliation:

1. Max Planck Institute for Gravitational Physics (Albert Einstein Institute)

2. University of Southampton

Abstract

Geodesic scattering of a test particle off a Schwarzschild black hole can be parametrized by the speed-at-infinity v and the impact parameter b, with a “separatrix,” b=bc(v), marking the threshold between scattering and plunge. Near the separatrix, the scattering angle diverges as log(bbc). The self-force correction to the scattering angle (at fixed v, b) diverges even faster, like A1(v)bc/(bbc). Here we numerically calculate the divergence coefficient A1(v) in a scalar-charge toy model. We then use our knowledge of A1(v) to inform a resummation of the post-Minkowskian expansion for the scattering angle, and demonstrate that the resummed series agrees remarkably well with numerical self-force results even in the strong-field regime. We propose that a similar resummation technique, applied to a mass particle subject to a gravitational self-force, can significantly enhance the utility and regime of validity of post-Minkowskian calculations for black-hole scattering. Published by the American Physical Society 2024

Funder

Engineering and Physical Sciences Research Council

University of Southampton

Publisher

American Physical Society (APS)

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