TY - JOUR

T1 - Numerical analysis of quasinormal modes in nearly extremal Schwarzschild–de Sitter spacetimes

AU - Yoshida, Shijun

AU - Futamase, Toshifumi

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2004

Y1 - 2004

N2 - 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 [Formula Presented] is small enough, where [Formula Presented] and [Formula Presented] 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 [Formula Presented] 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-Nordström black hole. The amplitude of oscillating [Formula Presented] as a function of [Formula Presented] approaches a nonzero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where [Formula Presented] 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.

AB - 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 [Formula Presented] is small enough, where [Formula Presented] and [Formula Presented] 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 [Formula Presented] 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-Nordström black hole. The amplitude of oscillating [Formula Presented] as a function of [Formula Presented] approaches a nonzero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where [Formula Presented] 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.

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U2 - 10.1103/PhysRevD.69.064025

DO - 10.1103/PhysRevD.69.064025

M3 - Article

AN - SCOPUS:2342423354

VL - 69

SP - 7

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 6

ER -