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Gravitational self-force from radiation-gauge metric perturbations

Gravitational self-force from radiation-gauge metric perturbations
Gravitational self-force from radiation-gauge metric perturbations
Calculations of the gravitational self-force (GSF) on a point mass in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the metric perturbation is formulated in a class of “radiation” gauges, in which the particle singularity is nonisotropic and extends away from the particle’s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We show that three types of radiation gauge exist: two containing a radial stringlike singularity emanating from the particle, either in one direction (“half-string” gauges) or both directions (“full-string” gauges); and a third type containing no strings but with a jump discontinuity (and possibly a delta function) across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the “regular half” of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, which is analogous to the standard Lorenz-gauge formula but requires a correction to the values of the regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the regularization parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla’s invariance theorem for the regularization parameters, and we discuss the correspondence between our method and a related approach by Friedman et al.
1550-7998
24009
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Merlin, Cesar
9b55102d-7650-4e9f-9277-eff84ca08983
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Merlin, Cesar
9b55102d-7650-4e9f-9277-eff84ca08983
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Pound, Adam, Merlin, Cesar and Barack, Leor (2014) Gravitational self-force from radiation-gauge metric perturbations. Physical Review D, 89 (2), 24009. (doi:10.1103/PhysRevD.89.024009).

Record type: Article

Abstract

Calculations of the gravitational self-force (GSF) on a point mass in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the metric perturbation is formulated in a class of “radiation” gauges, in which the particle singularity is nonisotropic and extends away from the particle’s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We show that three types of radiation gauge exist: two containing a radial stringlike singularity emanating from the particle, either in one direction (“half-string” gauges) or both directions (“full-string” gauges); and a third type containing no strings but with a jump discontinuity (and possibly a delta function) across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the “regular half” of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, which is analogous to the standard Lorenz-gauge formula but requires a correction to the values of the regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the regularization parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla’s invariance theorem for the regularization parameters, and we discuss the correspondence between our method and a related approach by Friedman et al.

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PhysRevD.89.024009 - Version of Record
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e-pub ahead of print date: 9 January 2014
Published date: 2014
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 369457
URI: https://eprints.soton.ac.uk/id/eprint/369457
ISSN: 1550-7998
PURE UUID: 22d8390c-b389-4dab-9656-e1c46730bbac
ORCID for Leor Barack: ORCID iD orcid.org/0000-0003-4742-9413

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Date deposited: 26 Sep 2014 13:28
Last modified: 22 Oct 2019 00:44

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