2003/08/31 by Shijun Yoshida, Toshifumi Futamase
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #De Sitter universe #General relativity #Gravitation #Horizon #Limit (mathematics) #Mathematical analysis #Mathematical physics #Omega #Order (exchange) #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Quasinormal mode #Schwarzschild metric #Schwarzschild radius #Universe #gr-qc
paper · pdf · doi:10.1103/physrevd.69.064025
published as Phys.Rev. D69 (2004) 064025 · 9 pages, 7 figures, to appear in Physical Review D
arxiv created 2004/01/22 · openalex publication_date 2004/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We calculate high-order quasinormal modes with large imaginary frequencies for electromagnetic and gravitational perturbations in nearly extremal Schwarzschild--de Sitter spacetimes. Our results show that for low-order quasinormal modes the analytical approximation formula in the extremal limit derived by Cardoso and Lemos is quite a good approximation for the quasinormal frequencies as long as the model parameter r1\ensuremathκ1 is small enough, where r1 and \ensuremathκ1 are the black hole horizon radius and the surface gravity, respectively. For high-order quasinormal modes, to which correspond quasinormal frequencies with large imaginary parts, on the other hand, this formula becomes inaccurate even for small values of r1\ensuremathκ1. We also find that the real parts of the quasinormal frequencies have oscillating behaviors in the limit of highly damped modes, which are similar to those observed in the case of a Reissner-Nordstr"om black hole. The amplitude of oscillating Re(\mathrm\ensuremathω) as a function of Im(\ensuremathω) approaches a nonzero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where \ensuremathω denotes the quasinormal frequency. This means that for gravitational perturbations the real part of the quasinormal modes of the nearly extremal Schwarzschild--de Sitter spacetime appears not to approach any constant value in the limit of highly damped modes. On the other hand, for electromagnetic perturbations, the real part of the frequency seems to go to zero in the limit.