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Prog. Theor. Phys. Vol. 100 No. 3 (1998) pp. 491-505

Perturbations of Kerr-de Sitter Black Holes and Heun's Equations

Hisao Suzuki,^*) Eiichi Takasugi^†,**) and Hiroshi Umetsu^†,***)

Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
^†Department of Physics, Osaka University, Toyonaka 560-0043, Japan

(Received May 26, 1998)

Abstract:

It is well known that the perturbation equations of massless fields for the Kerr-de Sitter geometry can be written in the form of separable equations. The equations have five definite singularities, so it has been thought that their analysis would be difficult. We show that these equations can be transformed into Heun's equations, for which we are able to use a known technique to analyze solutions. We reproduce known results for the Kerr geometry and de Sitter geometry in the confluent limits of Heun's functions. Our analysis can be extended to Kerr-Newman-de Sitter geometry for massless fields with spin 0 and 1/2.

URL : http://ptp.ipap.jp/link?PTP/100/491/
DOI : 10.1143/PTP.100.491

^*)E-mail: hsuzuki@particle.sci.hokudai.ac.jp
^**)E-mail: takasugi@phys.wani.osaka-u.ac.jp
^***)E-mail: umetsu@phys.wani.osaka-u.ac.jp

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 102 No. 2 (1999) pp. 253-272 :

   Analytic Solutions of the Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries

   Hisao Suzuki, Eiichi Takasugi and Hiroshi Umetsu

2. Progress of Theoretical Physics Vol. 103 No. 4 (2000) pp. 723-731 :

   Absorption Rate of the Kerr-de Sitter Black Hole and the Kerr-Newman-de Sitter Black Hole

   Hisao Suzuki, Eiichi Takasugi and Hiroshi Umetsu

3. Progress of Theoretical Physics Vol. 104 No. 4 (2000) pp. 743-755 :

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

   Hiroshi Umetsu

4. Progress of Theoretical Physics Vol. 128 No. 2 (2012) pp. 227-241 :

   Scalar Spheroidal Harmonics in Five Dimensional Kerr-(A)dS

   H. T. Cho, Alan S. Cornell, Jason Doukas and Wade Naylor

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