Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

Details Reconstruction of Black Hole Metric Perturbations from Weyl Curvature Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

2002-03-18

arxiv.org/abs/gr-qc/0203061v1

Phys.Rev. D66 (2002) 024026

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 Pages, Revtex4

Scientific paper

10.1103/PhysRevD.66.024026

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $\psi_4$ and $\psi_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $\Psi$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $\psi_4$ and $\psi_0$. We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.

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