The University of Southampton
University of Southampton Institutional Repository

Completion of metric reconstruction for a particle orbiting a Kerr black hole

Completion of metric reconstruction for a particle orbiting a Kerr black hole
Completion of metric reconstruction for a particle orbiting a Kerr black hole
Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in
either of the two Weyl scalars ? 0 or ? 4 , using a procedure described by Chrzanowski and others in the
1970s. More recent work, motivated within the context of self-force physics, extends the procedure to
metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves
undetermined a certain stationary, axially symmetric piece of the metric perturbation. In the vacuum region
away from the particle, this “completion” piece corresponds simply to mass and angular-momentum
perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here, we
present and implement a rigorous method for finding the completion piece. The key idea is to impose
continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed)
perturbation, in order to determine the unknown amplitude parameters of the completion piece. We
implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black
hole. Our results provide a rigorous underpinning of recent results by Friedman et al. for circular orbits and
extend them to noncircular orbits.
1550-7998
1-29
Merlin Gonzalez, Cesar
84fdb9a9-22b8-4d96-a3a6-6d61e912d799
Ori, Amos
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Van De Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22
Merlin Gonzalez, Cesar
84fdb9a9-22b8-4d96-a3a6-6d61e912d799
Ori, Amos
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Van De Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22

Merlin Gonzalez, Cesar, Ori, Amos, Pound, Adam and Van De Meent, Maarten (2016) Completion of metric reconstruction for a particle orbiting a Kerr black hole. Physical Review D, 94 (104066), 1-29. (doi:10.1103/PhysRevD.94.104066).

Record type: Article

Abstract

Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in
either of the two Weyl scalars ? 0 or ? 4 , using a procedure described by Chrzanowski and others in the
1970s. More recent work, motivated within the context of self-force physics, extends the procedure to
metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves
undetermined a certain stationary, axially symmetric piece of the metric perturbation. In the vacuum region
away from the particle, this “completion” piece corresponds simply to mass and angular-momentum
perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here, we
present and implement a rigorous method for finding the completion piece. The key idea is to impose
continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed)
perturbation, in order to determine the unknown amplitude parameters of the completion piece. We
implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black
hole. Our results provide a rigorous underpinning of recent results by Friedman et al. for circular orbits and
extend them to noncircular orbits.

Text
completion.pdf - Accepted Manuscript
Download (572kB)
Text
PhysRevD.94.104066.pdf - Version of Record
Restricted to Repository staff only
Request a copy

More information

Submitted date: 4 September 2016
Accepted/In Press date: 27 October 2016
e-pub ahead of print date: 28 November 2016
Published date: 28 November 2016
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 405570
URI: http://eprints.soton.ac.uk/id/eprint/405570
ISSN: 1550-7998
PURE UUID: ebf73700-ea82-4561-858a-1c05e4cd3bad
ORCID for Amos Ori: ORCID iD orcid.org/0000-0003-4742-9413
ORCID for Adam Pound: ORCID iD orcid.org/0000-0001-9446-0638

Catalogue record

Date deposited: 07 Feb 2017 16:24
Last modified: 16 Mar 2024 04:09

Export record

Altmetrics

Contributors

Author: Cesar Merlin Gonzalez
Author: Amos Ori ORCID iD
Author: Adam Pound ORCID iD
Author: Maarten Van De Meent

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×