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", $b=b_c(v)$, 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.

15 pages, 9 figures; v2 minor typographic changes; v3 minor edits to match published version

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• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• Black-hole scattering with numerical relativity: Self-force extraction and post-Minkowskian validation
• Relieving scale disparity in binary black hole simulations
• Gravitational scattering of two neutron stars
• Constants of motion in gravitational self-force theory
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits
• Frequency-domain self-force calculations using Gegenbauer reconstruction