A Conserved Energy Integral for Perturbation Equations in the Kerr-de Sitter Geometry

Details A Conserved Energy Integral for Perturbation Equations in the Kerr-de Sitter Geometry A Conserved Energy Integral for Perturbation Equations in the Kerr-de Sitter Geometry

2000-05-11

arxiv.org/abs/gr-qc/0005037v1

Prog.Theor.Phys. 104 (2000) 743-755

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, LaTeX

Scientific paper

10.1143/PTP.104.743

The analytic proof of mode stability of the Kerr black hole was provided by Whiting. In his proof, the construction of a conserved quantity for unstable mode was crucial. We extend the method of the analysis for 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 the equations. Using those we construct a conserved quantity for unstable modes in the Kerr-de Sitter geometry, and discuss its property.

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