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Perturbations of Schwarzschild black holes in the Lorenz gauge: formulation and numerical implementation

Perturbations of Schwarzschild black holes in the Lorenz gauge: formulation and numerical implementation
Perturbations of Schwarzschild black holes in the Lorenz gauge: formulation and numerical implementation
We reformulate the theory of Schwarzschild black hole perturbations in terms of the metric perturbation in the Lorenz gauge. In this formulation, each tensor-harmonic mode of the perturbation is constructed algebraically from ten scalar functions, satisfying a set of ten wavelike equations, which are decoupled at their principal parts. We solve these equations using numerical evolution in the time domain, for the case of a pointlike test particle set in a circular geodesic orbit around the black hole. Our code uses characteristic coordinates, and incorporates a constraint-damping scheme. The axially symmetric, odd-parity modes of the perturbation are obtained analytically. The approach developed here is especially advantageous in applications requiring knowledge of the local metric perturbation near a point particle; in particular, it offers a useful framework for calculations of the gravitational self-force.
1550-7998
104026-[25pp]
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Lousto, Carlos O.
afa05f00-0bf8-4ecc-8ac4-0506e1feda03
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Lousto, Carlos O.
afa05f00-0bf8-4ecc-8ac4-0506e1feda03

Barack, Leor and Lousto, Carlos O. (2005) Perturbations of Schwarzschild black holes in the Lorenz gauge: formulation and numerical implementation. Physical Review D, 72 (10), 104026-[25pp]. (doi:10.1103/PhysRevD.72.104026).

Record type: Article

Abstract

We reformulate the theory of Schwarzschild black hole perturbations in terms of the metric perturbation in the Lorenz gauge. In this formulation, each tensor-harmonic mode of the perturbation is constructed algebraically from ten scalar functions, satisfying a set of ten wavelike equations, which are decoupled at their principal parts. We solve these equations using numerical evolution in the time domain, for the case of a pointlike test particle set in a circular geodesic orbit around the black hole. Our code uses characteristic coordinates, and incorporates a constraint-damping scheme. The axially symmetric, odd-parity modes of the perturbation are obtained analytically. The approach developed here is especially advantageous in applications requiring knowledge of the local metric perturbation near a point particle; in particular, it offers a useful framework for calculations of the gravitational self-force.

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Published date: 2005

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Local EPrints ID: 29373
URI: http://eprints.soton.ac.uk/id/eprint/29373
ISSN: 1550-7998
PURE UUID: 25ac9322-48e6-4a3d-940f-263d9c373c94
ORCID for Leor Barack: ORCID iD orcid.org/0000-0003-4742-9413

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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 03:41

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Contributors

Author: Leor Barack ORCID iD
Author: Carlos O. Lousto

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