Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model

Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model

Using self-force methods, we consider the hyperbolic-type scattering of a pointlike particle carrying a scalar charge $Q$ off a Schwarzschild black hole. For given initial velocity and impact parameter, back-reaction from the scalar field modifies the scattering angle by an amount $\propto\! Q^2$, which we calculate numerically for a large sample of orbits (neglecting the gravitational self-force). Our results probe both strong-field and field-weak scenarios, and in the latter case we find a good agreement with post-Minkowskian expressions. The scalar-field self-force has a component tangent to the four-velocity that exchanges particle's mass with scalar-field energy, and we also compute this mass exchange as a function along the orbit. The expressions we derive for the scattering angle (in terms of certain integrals of the self-force along the orbit) can be used to obtain the gravitational self-force correction to the angle in the physical problem of a binary black hole with a large mass ratio. We discuss the remaining steps necessary to achieve this goal.

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Long, Oliver

e20e8ea1-61c1-4998-9bf1-6938e7b8cdcb

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Long, Oliver

e20e8ea1-61c1-4998-9bf1-6938e7b8cdcb

[Unknown type: UNSPECIFIED]

## Abstract

Using self-force methods, we consider the hyperbolic-type scattering of a pointlike particle carrying a scalar charge $Q$ off a Schwarzschild black hole. For given initial velocity and impact parameter, back-reaction from the scalar field modifies the scattering angle by an amount $\propto\! Q^2$, which we calculate numerically for a large sample of orbits (neglecting the gravitational self-force). Our results probe both strong-field and field-weak scenarios, and in the latter case we find a good agreement with post-Minkowskian expressions. The scalar-field self-force has a component tangent to the four-velocity that exchanges particle's mass with scalar-field energy, and we also compute this mass exchange as a function along the orbit. The expressions we derive for the scattering angle (in terms of certain integrals of the self-force along the orbit) can be used to obtain the gravitational self-force correction to the angle in the physical problem of a binary black hole with a large mass ratio. We discuss the remaining steps necessary to achieve this goal.

Text

** 2209.03740
- Author's Original**
## More information

e-pub ahead of print date: 2022

## Identifiers

Local EPrints ID: 471633

URI: http://eprints.soton.ac.uk/id/eprint/471633

PURE UUID: 822f549a-89f9-4675-9bee-c2be3a79ab88

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Date deposited: 15 Nov 2022 17:50

Last modified: 16 Nov 2022 02:58

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## Contributors

Author:
Oliver Long
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