Open AccessA Conserved Energy Integral for Perturbation Equations in the Kerr-de Sitter Geometry
Author(s) -
H. Umetsu
Publication year - 2000
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.104.743
Subject(s) - physics , de sitter universe , massless particle , conserved quantity , gravitational singularity , perturbation (astronomy) , anti de sitter space , mathematical physics , classical mechanics , geometry , quantum mechanics , mathematics , universe
The analytic proof of mode stability of the Kerr black hole was provided byWhiting. In his proof, the construction of a conserved quantity for unstablemode was crucial. We extend the method of the analysis for the Kerr-de Sittergeometry. The perturbation equations of massless fields in the Kerr-de Sittergeometry can be transformed into Heun's equations which have four regularsingularities. In this paper we investigate differential and integraltransformations of solutions of the equations. Using those we construct aconserved quantity for unstable modes in the Kerr-de Sitter geometry, anddiscuss its property.Comment: 13 pages, LaTe
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