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

TL;DR

This paper investigates the divergence of scattering angles near the black hole plunge threshold, computes self-force corrections in a scalar model, and introduces a resummation method to improve post-Minkowskian predictions in strong gravity regimes.

Contribution

It introduces a resummation technique for post-Minkowskian series informed by self-force calculations, extending their accuracy near the plunge threshold in black hole scattering.

Findings

Resummed series matches numerical self-force results well in strong-field regimes.

Self-force divergence coefficient $A_1(v)$ computed in a scalar-charge toy model.

Resummation enhances the applicability of post-Minkowskian calculations for black-hole scattering.

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", $b=b_c(v)$, marking the threshold between scattering and plunge. Near the separatrix, the scattering angle diverges as $\sim\log(b-b_c)$. The self-force correction to the scattering angle (at fixed $v,b$) diverges even faster, like $\sim A_1(v)b_c/(b-b_c)$. Here we numerically calculate the divergence coefficient $A_1(v)$ in a scalar-charge toy model. We then use our knowledge of $A_1(v)$ 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.