High overtones of Schwarzschild - de - Sitter quasinormal spectrum

We find the high overtones of gravitational and electromagnetic quasi-normal 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 → ∞ but rather some oscillating function. The spacing for imaginary part Im(ω n+1) − Im(ω n) for electromagnetic perturbations at high n slowly approach k e as n → ∞, 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.