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

Abstract

Geodesic scattering of a test particle off a Schwarzschild black hole can be parameterized 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(b−bc). The self-force correction to the scattering angle (at fixed v,b) diverges even faster, like ∼A1(v)bc/(b−bc). 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.

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Identifiers

ORCID for Oliver Long: orcid.org/0000-0002-3897-9272

ORCID for Christopher Whittall: orcid.org/0000-0003-2152-6004

ORCID for Leor Barack: orcid.org/0000-0003-4742-9413

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