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

Details 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

2005-10-05

arxiv.org/abs/gr-qc/0510019v2

Phys.Rev. D72 (2005) 104026

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages, 21 eps figures

Scientific paper

10.1103/PhysRevD.72.104026

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 10 scalar functions, satisfying a set of 10 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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