Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge

Details Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge

2005-01-27

arxiv.org/abs/gr-qc/0501088v2

Class.Quant.Grav. 22 (2005) S569-S588

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, no figures

Scientific paper

10.1088/0264-9381/22/15/002

Perturbation theory of rotating black holes is described in terms of the Weyl scalars $\psi_4$ and $\psi_0$; each satisfying the Teukolsky's complex master wave equation with spin $s=\mp2$, and respectively representing outgoing and ingoing radiation. We explicitly construct the metric perturbations out of these Weyl scalars in the Regge-Wheeler gauge in the nonrotating limit. We propose a generalization of the Regge-Wheeler gauge for Kerr background in the Newman-Penrose language, and discuss the approach for building up the perturbed spacetime of a rotating black hole. We also provide both-way relationships between waveforms defined in the metric and curvature approaches in the time domain, also known as the (inverse-) Chandrasekhar transformations, generalized to include matter.

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