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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

References

[1]Bardeen, J. M. and Press, W. H., “Radiation fields in the Schwarzschild background”, J. Math. Phys. 14 (1973) 7–19.CrossRefGoogle Scholar
[2]Chandrasekhar, S., The Mathematical Theory of Black Holes (Oxford University Press, New York, 1983).Google Scholar
[3]Fernandes, J. F. Q. and Lun, A. W. C., J. Math. Phys. submitted.Google Scholar
[4]Fernandes, J. F. Q. and Lun, A. W. C., in Proceedings of the Seventh Marcel Grossmann Meeting on General Relativity, (to appear).Google Scholar
[5]Lun, A. W. C., Ph. D. Thesis, Monash University, 1976.Google Scholar
[6]Lun, A. W.-C. and Fackerell, E. D., “A master equation for perturbations to the Schwarzschild geometry”, Lett. Cimento 9 (1974) 599–602.CrossRefGoogle Scholar
[7]Penrose, R. and Rindler, W., Spinors and Space-time. Volume 1 (Cambridge University Press, Cambridge, 1984).CrossRefGoogle Scholar
[8]Price, R. H., “Nonspherical perturbations of relativistic gravitational collapse. I Scalar and gravitational perturbations”, Phys. Rev. D 5 (1972) 2419–2438.CrossRefGoogle Scholar
[9]Price, R. H., “Nonspherical perturbations of relativistic gravitational collapse. II Integer-spin, zero-rest-mass-fields”, Phys. Rev. D 5 (1972) 2439–2454.CrossRefGoogle Scholar
[10], T. Regge and Wheeler, J. A., “Stability of Schwarzschild singularity”, Phys. Rev. 108 (1957) 1063.CrossRefGoogle Scholar
[11]Sasaki, M. and Nakamura, T., “Gravitational radiation from a Kerr black hole. I – Formulation and a method for numerical analysis”, Prog. Theor. Phys. 67 (1982) 1788–1809.CrossRefGoogle Scholar
[12]Teukolsky, S. A. and Press, W. H., “Perturbations od a rotating black hole. III. interaction of the hole with gravitational and electromagnetic radiation”, Astroph. J. 193 (1974) 443–461.CrossRefGoogle Scholar