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 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 diverg...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Long, Oliver, Whittall, Christopher, Barack, Leor
Format: Article
Language:English
Subjects:
Divergence
Scattering angle
Online Access:Get full text
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Summary: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.
ISSN:2331-8422