Wave and stability properties of black holes |
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Authors: | J. F. McKenzie J. D. Krige |
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Affiliation: | (1) Department of Mathematics and Applied Mathematics, University of Natal, Durban, South Africa |
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Abstract: | In this paper we transform the wave equation governing gravitational perturbations of a Schwarzschild black hole from its standard Schrödinger or Regge-Wheeler form to a Klein-Gordon type wave equation. This latter form reveals immediately that incoming waves with frequencies ()cml , a critical frequency, are completely reflected (transmitted). This process is entirely due to the radial variation of the cut-off frequency inherent in the dispersive nature of the wave propagation properties of gravitational perturbations of the Schwarzschild metric. Moreover, those high-frequency waves (cml) which penetrate through the region near the Schwarzschild radiusrsare, on crossing this event horizon, attenuated by a factor exp (–rs/c), thereby dumping most of their energy and momentum into the black hole. It is shown that in the vicinity ofrsthe metric is locally unstable. This feature and the wave absorption process indicate that the neighbourhood aroundrsis dynamically active, and, as well as acting like a Hawking-type particle creator, will behave as a wave emitter in order to relax the stresses on the metric. |
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