Frequency-domain approach to self-force in hyperbolic scattering
Frequency-domain approach to self-force in hyperbolic scattering
We develop a frequency-domain method for calculating the self-force acting on a scalar charge on a fixed scattering geodesic in Schwarzschild spacetime. Existing frequency-domain methods, which are tailored for bound orbits, are inadequate here for several reasons. One must account for the continuous spectrum in the scattering problem, deal with slowly convergent radial integrals that are hard to evaluate numerically, and confront the inapplicability of the standard self-force method of “extended homogeneous solutions,” which only works for compactly supported sources. We tackle each of these issues in turn, and then present a full numerical implementation, in which we calculate the self-force correction to the scatter angle due to scalar-field backreaction. We perform a range of internal validation tests, as well as ones based on comparison with existing time-domain results. We discuss the merits and remaining limitations of our method, and outline directions for future work.
Whittall, Christopher Luke
71258c6b-072f-44a2-85c9-67ada32fe7c7
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
11 September 2023
Whittall, Christopher Luke
71258c6b-072f-44a2-85c9-67ada32fe7c7
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Whittall, Christopher Luke and Barack, Leor
(2023)
Frequency-domain approach to self-force in hyperbolic scattering.
Physical Review D, 108 (6-15), [064017].
(doi:10.1103/PhysRevD.108.064017).
Abstract
We develop a frequency-domain method for calculating the self-force acting on a scalar charge on a fixed scattering geodesic in Schwarzschild spacetime. Existing frequency-domain methods, which are tailored for bound orbits, are inadequate here for several reasons. One must account for the continuous spectrum in the scattering problem, deal with slowly convergent radial integrals that are hard to evaluate numerically, and confront the inapplicability of the standard self-force method of “extended homogeneous solutions,” which only works for compactly supported sources. We tackle each of these issues in turn, and then present a full numerical implementation, in which we calculate the self-force correction to the scatter angle due to scalar-field backreaction. We perform a range of internal validation tests, as well as ones based on comparison with existing time-domain results. We discuss the merits and remaining limitations of our method, and outline directions for future work.
Text
PhysRevD.108.064017
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Accepted/In Press date: 25 July 2023
Published date: 11 September 2023
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Funding Information:
We are deeply grateful to Oliver Long for producing and providing comparison data from his time-domain code, and for his useful comments and advice throughout this work. We also thank Maarten van de Meent and Niels Warburton for useful discussions. C. W. acknowledges support from EPSRC through Grant No. EP/V520056/1. This work makes use of the Black Hole Perturbation Toolkit.
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© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
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Local EPrints ID: 482245
URI: http://eprints.soton.ac.uk/id/eprint/482245
ISSN: 2470-0010
PURE UUID: 78be8ab6-634e-4c16-a6ec-0249a526c1c0
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Date deposited: 22 Sep 2023 16:31
Last modified: 18 Mar 2024 03:58
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