2000/05/11 by H. Umetsu, Hiroshi Umetsu
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1143/ptp.104.743
published as Prog.Theor.Phys. 104 (2000) 743-755 · 13 pages, LaTeX
arxiv created 2000/05/11 · openalex publication_date 2000/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.