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Second-order gravitational self-force in a highly regular gauge

Second-order gravitational self-force in a highly regular gauge
Second-order gravitational self-force in a highly regular gauge

Extreme-mass-ratio inspirals (EMRIs) will be key sources for LISA. However, accurately extracting system parameters from a detected EMRI waveform will require self-force calculations at second order in perturbation theory, which are still in a nascent stage. One major obstacle in these calculations is the strong divergences that are encountered on the worldline of the small object. Previously, it was shown by one of us [A. Pound, Nonlinear gravitational self-force: Second-order equation of motion, Phys. Rev. D 95, 104056 (2017)PRVDAQ2470-001010.1103/PhysRevD.95.104056] that a class of "highly regular"gauges exist in which the singularities have a qualitatively milder form, promising to enable more efficient numerical calculations. Here we derive expressions for the metric perturbation in this class of gauges, in a local expansion in powers of distance r from the worldline, to sufficient order in r for numerical implementation in a puncture scheme. Additionally, we use the highly regular class to rigorously derive a distributional source for the second-order field and a pointlike second-order stress-energy tensor (the Detweiler stress energy) for the small object. This makes it possible to calculate the second-order self-force using mode-sum regularization rather than the more cumbersome puncture schemes that have been necessary.

1550-7998
Upton, Samuel D.
9afe447b-462b-4be8-9694-d8c5726fe020
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Upton, Samuel D.
9afe447b-462b-4be8-9694-d8c5726fe020
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70

Upton, Samuel D. and Pound, Adam (2021) Second-order gravitational self-force in a highly regular gauge. Physical Review D, 103 (12), [124016]. (doi:10.1103/PhysRevD.103.124016).

Record type: Article

Abstract

Extreme-mass-ratio inspirals (EMRIs) will be key sources for LISA. However, accurately extracting system parameters from a detected EMRI waveform will require self-force calculations at second order in perturbation theory, which are still in a nascent stage. One major obstacle in these calculations is the strong divergences that are encountered on the worldline of the small object. Previously, it was shown by one of us [A. Pound, Nonlinear gravitational self-force: Second-order equation of motion, Phys. Rev. D 95, 104056 (2017)PRVDAQ2470-001010.1103/PhysRevD.95.104056] that a class of "highly regular"gauges exist in which the singularities have a qualitatively milder form, promising to enable more efficient numerical calculations. Here we derive expressions for the metric perturbation in this class of gauges, in a local expansion in powers of distance r from the worldline, to sufficient order in r for numerical implementation in a puncture scheme. Additionally, we use the highly regular class to rigorously derive a distributional source for the second-order field and a pointlike second-order stress-energy tensor (the Detweiler stress energy) for the small object. This makes it possible to calculate the second-order self-force using mode-sum regularization rather than the more cumbersome puncture schemes that have been necessary.

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HR_gauge_and_self_force_motion - Accepted Manuscript
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Submitted date: 27 January 2021
Accepted/In Press date: 6 May 2021
Published date: 7 June 2021
Additional Information: Funding Information: This work was supported by a Royal Society University Research Fellowship and a Royal Society Research Grant for Research Fellows. Publisher Copyright: © 2021 American Physical Society.

Identifiers

Local EPrints ID: 449072
URI: http://eprints.soton.ac.uk/id/eprint/449072
ISSN: 1550-7998
PURE UUID: 4fa8ccd0-a86a-491b-be7a-0bd1f51902c5
ORCID for Samuel D. Upton: ORCID iD orcid.org/0000-0003-2965-7674
ORCID for Adam Pound: ORCID iD orcid.org/0000-0001-9446-0638

Catalogue record

Date deposited: 14 May 2021 16:33
Last modified: 24 May 2024 01:44

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