Black hole scattering near the transition to plunge: self-force and resummation of post-Minkowskian theory
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=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.
Long, Oliver
e20e8ea1-61c1-4998-9bf1-6938e7b8cdcb
Whittall, Christopher
71258c6b-072f-44a2-85c9-67ada32fe7c7
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
21 August 2024
Long, Oliver
e20e8ea1-61c1-4998-9bf1-6938e7b8cdcb
Whittall, Christopher
71258c6b-072f-44a2-85c9-67ada32fe7c7
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Long, Oliver, Whittall, Christopher and Barack, Leor
(2024)
Black hole scattering near the transition to plunge: self-force and resummation of post-Minkowskian theory.
arXiv, 110.
(doi:10.48550/arXiv.2406.08363).
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=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.
Text
2406.08363v2
- Author's Original
Available under License Other.
Text
PhysRevD.110.044039
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Accepted/In Press date: 12 June 2024
Published date: 21 August 2024
Identifiers
Local EPrints ID: 503598
URI: http://eprints.soton.ac.uk/id/eprint/503598
ISSN: 2331-8422
PURE UUID: aeff48e8-b43d-4957-ab63-c1ab04513602
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Date deposited: 06 Aug 2025 16:46
Last modified: 22 Aug 2025 01:53
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Oliver Long
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