Second-order gravitational self-force in a highly regular gauge: covariant and coordinate punctures
Second-order gravitational self-force in a highly regular gauge: covariant and coordinate punctures
Gravitational self-force theory is the primary way of modelling extreme-mass-ratio inspirals (EMRIs). One difficulty that appears in second-order self-force calculations is the strong divergence at the worldline of the small object, which causes both numerical and analytical issues. Previous work [Phys. Rev. D 95, 104056 (2017); ibid. 103, 124016 (2021)] demonstrated that this could be alleviated within a class of highly regular gauges and presented the metric perturbations in these gauges in a local coordinate form. We build on this previous work by deriving expressions for the highly regular gauge metric perturbations in both fully covariant form and as a generic coordinate expansion. With the metric perturbations in covariant or generic coordinate form, they can easily be expressed in any convenient coordinate system. These results can then be used as input into a puncture scheme in order to solve the field equations describing an EMRI.
gr-qc
Upton, Samuel D.
f0ff8ac2-2ef0-4a99-b2d6-e55772f34dcf
8 February 2024
Upton, Samuel D.
f0ff8ac2-2ef0-4a99-b2d6-e55772f34dcf
Upton, Samuel D.
(2024)
Second-order gravitational self-force in a highly regular gauge: covariant and coordinate punctures.
Phys. Rev. D, 109 (4), [044021].
(doi:10.1103/PhysRevD.109.044021).
Abstract
Gravitational self-force theory is the primary way of modelling extreme-mass-ratio inspirals (EMRIs). One difficulty that appears in second-order self-force calculations is the strong divergence at the worldline of the small object, which causes both numerical and analytical issues. Previous work [Phys. Rev. D 95, 104056 (2017); ibid. 103, 124016 (2021)] demonstrated that this could be alleviated within a class of highly regular gauges and presented the metric perturbations in these gauges in a local coordinate form. We build on this previous work by deriving expressions for the highly regular gauge metric perturbations in both fully covariant form and as a generic coordinate expansion. With the metric perturbations in covariant or generic coordinate form, they can easily be expressed in any convenient coordinate system. These results can then be used as input into a puncture scheme in order to solve the field equations describing an EMRI.
Text
2309.03778v2
- Accepted Manuscript
Text
PhysRevD.109.044021
- Version of Record
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Submitted date: 7 September 2023
Accepted/In Press date: 14 December 2023
Published date: 8 February 2024
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© 2024 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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gr-qc
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Local EPrints ID: 490039
URI: http://eprints.soton.ac.uk/id/eprint/490039
ISSN: 2470-0010
PURE UUID: bb202349-5a36-4374-9b7f-1d22313831a8
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Date deposited: 14 May 2024 16:30
Last modified: 30 Nov 2024 03:15
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Author:
Samuel D. Upton
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