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Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole

Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar ?4 using semianalytical methods. The metric perturbation is then reconstructed from ?4 in an (outgoing) radiation gauge, adding the appropriate nonradiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift U as a function of the orbital frequencies ?r and ?? to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of U. In Kerr, we provide completely novel values of U for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.
1550-7998
1-26
Van De Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22
Shah, Abhay G.
fd7fde62-0589-4231-8797-2d20fe995389
Van De Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22
Shah, Abhay G.
fd7fde62-0589-4231-8797-2d20fe995389

Van De Meent, Maarten and Shah, Abhay G. (2015) Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole. Physical Review D, 92 (6), 1-26. (doi:10.1103/PhysRevD.92.064025).

Record type: Article

Abstract

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar ?4 using semianalytical methods. The metric perturbation is then reconstructed from ?4 in an (outgoing) radiation gauge, adding the appropriate nonradiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift U as a function of the orbital frequencies ?r and ?? to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of U. In Kerr, we provide completely novel values of U for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.

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Accepted/In Press date: 4 May 2015
Published date: 17 September 2015
Organisations: Applied Mathematics

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Local EPrints ID: 397864
URI: http://eprints.soton.ac.uk/id/eprint/397864
ISSN: 1550-7998
PURE UUID: 080af92c-361b-488c-8cd6-8dac6fdcee52

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Date deposited: 08 Jul 2016 10:29
Last modified: 15 Mar 2024 01:24

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Contributors

Author: Maarten Van De Meent
Author: Abhay G. Shah

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