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Prog. Theor. Phys. Vol. 104 No. 4 (2000) pp. 743-755
A Conserved Energy Integral for Perturbation Equations in the Kerr-de Sitter Geometry
Hiroshi Umetsu*)
Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
(Received May 11, 2000)
Abstract:
An analytic proof of mode stability of the Kerr black hole was provided
by Whiting. In his proof, the construction of a conserved quantity
for the unstable mode was crucial.
We extend the method of this analysis to the Kerr-de Sitter geometry.
The perturbation equations of massless fields in the Kerr-de Sitter
geometry can be transformed into Heun's equations, which have four
regular singularities.
In this paper we investigate differential and integral transformations
of solutions of these equations.
Using these, we construct a conserved quantity for unstable modes
in the Kerr-de Sitter geometry,
and we find that this quantity cannot bound the magnitudes of
the time derivative of perturbations.
URL :
http://ptp.ipap.jp/link?PTP/104/743/
DOI : 10.1143/PTP.104.743
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