High overtones of Schwarzschild-de-Sitter quasinormal spectrum

R. A. Konoplya; A. Zhidenko

doi:10.1088/1126-6708/2004/06/037

paper

High overtones of Schwarzschild-de-Sitter quasinormal spectrum

arXiv:hep-th/0402080 · doi:10.1088/1126-6708/2004/06/037

Abstract

We find the high overtones of gravitational and electromagnetic quasinormal spectrum of the Schwarzschild-de Sitter black hole. The calculations show that the real parts of the electromagnetic modes asymptotically approach zero. The gravitational modes show more peculiar behavior at large $n$ : the real part oscillates as a function of imaginary even for very high overtones and these oscillations settles to some "profile" which just repeats itself with further increasing of the overtone number $n$ . This lets us judge that $R e ω$ is not a constant as $n \to \infty$ but rather some oscillating function. The spacing for imaginary part $I m ω_{n + 1} - I m ω_{n}$ for both gravitational and electromagnetic perturbations at high $n$ oscillates as a function of $n$ around the value $k_{e}$ , where $k_{e}$ is the surface gravity. In addition we find the lower QN modes for which the values obtained with numerical methods are in a very good agreement with those obtained through the 6th order WKB technique.

arXiv comment15 pages, 4figures, Latex format

High overtones of Schwarzschild-de-Sitter quasinormal spectrum

Abstract

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