Gauge-invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates

Olivier Sarbach and Manuel Tiglio
Phys. Rev. D 64, 084016 – Published 25 September 2001
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Abstract

We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the gauge-invariant part of the metric perturbations from the amplitudes obeying our generalized Regge-Wheeler and Zerilli equations, and vice-versa. We also give a general expression for the radiated energy at infinity, and establish a relation between our geometrical equations and the Teukolsky formalism. The results presented in this paper are expected to be useful for the close-limit approximation to black hole collisions, for the Cauchy perturbative matching problem, and for the study of isolated horizons.

  • Received 19 April 2001

DOI:https://doi.org/10.1103/PhysRevD.64.084016

©2001 American Physical Society

Authors & Affiliations

Olivier Sarbach*

  • Center for Gravitational Physics and Geometry, Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802

Manuel Tiglio

  • Center for Gravitational Physics and Geometry, Department of Physics, and Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, Pennsylvania 16802

  • *Email address: sarbach@gravity.phys.psu.edu
  • Email address: tiglio@gravity.phys.psu.edu

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Issue

Vol. 64, Iss. 8 — 15 October 2001

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