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

## 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.

- Authors:

- School of Mathematics, University of Southampton, Southampton, SO17 1BJ (United Kingdom)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20711579

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.104026; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AXIAL SYMMETRY; BLACK HOLES; COSMOLOGY; DAMPING; DIFFERENTIAL GEOMETRY; DISTURBANCES; LORENTZ INVARIANCE; PARITY; SCALARS; SCHWARZSCHILD METRIC; TENSORS; TEST PARTICLES

### Citation Formats

```
Barack, Leor, Lousto, Carlos O., and Department of Physics and Astronomy, and Center for Gravitational Wave Astronomy, The University of Texas at Brownsville, Brownsville, Texas 78520.
```*Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.104026.

```
Barack, Leor, Lousto, Carlos O., & Department of Physics and Astronomy, and Center for Gravitational Wave Astronomy, The University of Texas at Brownsville, Brownsville, Texas 78520.
```*Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation*. United States. doi:10.1103/PhysRevD.72.104026.

```
Barack, Leor, Lousto, Carlos O., and Department of Physics and Astronomy, and Center for Gravitational Wave Astronomy, The University of Texas at Brownsville, Brownsville, Texas 78520. Tue .
"Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation". United States.
doi:10.1103/PhysRevD.72.104026.
```

```
@article{osti_20711579,
```

title = {Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation},

author = {Barack, Leor and Lousto, Carlos O. and Department of Physics and Astronomy, and Center for Gravitational Wave Astronomy, The University of Texas at Brownsville, Brownsville, Texas 78520},

abstractNote = {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.},

doi = {10.1103/PhysRevD.72.104026},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}