Gravitational Perturbation of Schwarzschild-De Sitter Spacetime and Its Quasi-Normal Modes

We studied gravitational perturbation of Schwarzschild-de Sitter spacetime in the Newman-Penrose formalism. In particular we calculate the frequencies of quasi-normal modes based on the WKB approximation. It is found that the real as well as the imaginary part of the frequencies decreases as the increase of the cosmological constant, but the imaginary part remains positive even at the largest possible value for the cosmological constant. Thus the stability is established.