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Gravitational self force on a particle in circular orbit around a Schwarzschild black hole

Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
We calculate the gravitational self force acting on a pointlike test particle of mass ?, set in a circular geodesic orbit around a Schwarzschild black hole. Our calculation is done in the Lorenz gauge: For given orbital radius, we first solve directly for the Lorenz-gauge metric perturbation using numerical evolution in the time domain; We then compute the (finite) back-reaction force from each of the multipole modes of the perturbation; Finally, we apply the ``mode sum'' method to obtain the total, physical self force. The temporal component of the self force (which is gauge invariant) describes the dissipation of orbital energy through gravitational radiation. Our results for this component are consistent, to within the computational accuracy, with the total flux of gravitational-wave energy radiated to infinity and through the event horizon. The radial component of the self force (which is gauge dependent) is calculated here for the first time. It describes a conservative shift in the orbital parameters away from their geodesic values. We thus obtain the O(?) correction to the energy and angular momentum parameters (in the Lorenz gauge), as well as the O(?) shift in the orbital frequency (which is gauge invariant).
1550-7998
064021-[25pp]
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Sago, Norichika
50641559-f289-4ffa-810b-fe4ec8c26e26
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Sago, Norichika
50641559-f289-4ffa-810b-fe4ec8c26e26

Barack, Leor and Sago, Norichika (2007) Gravitational self force on a particle in circular orbit around a Schwarzschild black hole. Physical Review D, 75 (6), 064021-[25pp]. (doi:10.1103/PhysRevD.75.064021).

Record type: Article

Abstract

We calculate the gravitational self force acting on a pointlike test particle of mass ?, set in a circular geodesic orbit around a Schwarzschild black hole. Our calculation is done in the Lorenz gauge: For given orbital radius, we first solve directly for the Lorenz-gauge metric perturbation using numerical evolution in the time domain; We then compute the (finite) back-reaction force from each of the multipole modes of the perturbation; Finally, we apply the ``mode sum'' method to obtain the total, physical self force. The temporal component of the self force (which is gauge invariant) describes the dissipation of orbital energy through gravitational radiation. Our results for this component are consistent, to within the computational accuracy, with the total flux of gravitational-wave energy radiated to infinity and through the event horizon. The radial component of the self force (which is gauge dependent) is calculated here for the first time. It describes a conservative shift in the orbital parameters away from their geodesic values. We thus obtain the O(?) correction to the energy and angular momentum parameters (in the Lorenz gauge), as well as the O(?) shift in the orbital frequency (which is gauge invariant).

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More information

Submitted date: 15 January 2007
Published date: March 2007

Identifiers

Local EPrints ID: 43216
URI: https://eprints.soton.ac.uk/id/eprint/43216
ISSN: 1550-7998
PURE UUID: 7a1b1c70-bbcf-4a0c-b2bc-3299a8ae49ff

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Date deposited: 17 Jan 2007
Last modified: 13 Mar 2019 21:10

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