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 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(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. Published by the American Physical Society 2024