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Integrability conditions for the Bianchi identities as transformations in Schwarzschild space-time

Published online by Cambridge University Press:  17 February 2009

J. F. Q. Fernandes  and
A. W.-C. Lun
J. F. Q. Fernandes
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
A. W.-C. Lun
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
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Abstract

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We investigate the relationship between the Bardeen-Press and the Regge-Wheeler equations for perturbations of the Schwarzschild geometry. We examine how tetrad and coordinate gauge invariant Regge-Wheeler field quantities arise naturally from the perturbed Bianchi identities in the modified Newman-Penrose (compacted spincoefficient) formalism. The integrability conditions for the Bianchi identities then provide the transformation identities relating these quantities to the Bardeen-Press quantities. The relationships between the Bardeen-Press quantities of opposite spin-weight also arise naturally in our approach.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 2 , October 1999 , pp. 260 - 270
Copyright
Copyright © Australian Mathematical Society 1999

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