High overtones of Schwarzschild-de-Sitter quasinormal spectrum

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 Reω is not a constant as n → ∞ but rather some oscillating function. The spacing for imaginary part Imωn+1-Imωn for electromagnetic perturbations at high n slowly approach ke as n → ∞, 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. © SISSA/ISAS 2004.