Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes

Details Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes

2005-02-14

arxiv.org/abs/gr-qc/0502064v4

Class.Quant.Grav.22:R167,2005; Erratum-ibid.23:4297,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, no figures, published as Classical and Quantum Gravity topical review. Misprints present in the published version ar

Scientific paper

10.1088/0264-9381/22/16/R01 10.1

The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this paper is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of Schwarzschild black hole spacetimes driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes.

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