Olivier Sarbach, Manuel Tiglio
Published 2001-04-18, updated 2001-06-21Version 2
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 the 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.
Comments: Typos corrected. A small paragraph and two references added at the end of the Summary, Section II.C, concerning the case where matter fields are coupled to the metric. Some details have been included in the derivation of the radiated energy in section IV. Some references added. 21 pages, to appear in PRD
Journal: Phys.Rev. D64 (2001) 084016
SHORTCUT METHOD OF SOLUTION OF GEODESIC EQUATIONS FOR SCHWARZSCHILD BLACK HOLE
Calculation of gravitational wave forms from black hole collisions and disk collapse: Applying perturbation theory to numerical spacetimes
Black hole collisions from Brill-Lindquist initial data: predictions of perturbation theory
