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arXiv · hep-th/0402080

High overtones of Schwarzschild-de-Sitter quasinormal spectrum

R. A. Konoplya·A. Zhidenko
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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 $Re ω$ is not a constant as $n \to \infty$ but rather some oscillating function. The spacing for imaginary part $ Im ω_{n+1}-Im 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.

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R. A. Konoplya, A. Zhidenko. 2004-07-04. High overtones of Schwarzschild-de-Sitter quasinormal spectrum. https://doi.org/10.1088/1126-6708%2F2004%2F06%2F037

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