High Overtones of Schwarzschild de Sitter Quasinormal Spectrum

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 Reω is not a constant as n → ∞ but rather some oscillating function. The spacing for imaginary part Imωn+1 − Imωn for both gravitational and electromagnetic perturbations at high n oscillates as a function of n around the value ke, where ke 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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