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

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 = b c ( v ) , marking the threshold between scattering and plunge. Near the separatrix, the scattering angle diverges as ∼ log ( b − b c ) . The self-force correction to the scattering angle (at fixed v , b ) diverges even faster, like ∼ 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.