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
Long, Oliver
e20e8ea1-61c1-4998-9bf1-6938e7b8cdcb
Whittall, Christopher
71258c6b-072f-44a2-85c9-67ada32fe7c7
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
[Unknown type: UNSPECIFIED]
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.
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Accepted/In Press date: 12 June 2024
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Local EPrints ID: 492358
URI: http://eprints.soton.ac.uk/id/eprint/492358
PURE UUID: 02b7a0b5-7783-4ebb-ba21-a29175dc2c3e
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Date deposited: 24 Jul 2024 17:12
Last modified: 25 Jul 2024 01:59
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Author:
Oliver Long
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