Spectrums of Black Hole in de Sitter Spacetime with Highly Damped Quasinormal Modes: High Overtone Case

Motivated by recent physical interpretation on quasinormal modes presented by Maggiore, the adiabatic quantity method given by Kunstatter is used to calculate the spectrums of a non-extremal Schwarzschild de Sitter black hole in this paper, as well as electrically charged case. According to highly damped Konoplya and Zhidenko's numerical observational results for high overtone modes\cite{Konoplya}, we found that the asymptotic non-flat spacetime structure leads two interesting facts as followings: (i) near inner event horizon, the area and entropy spectrums, which are given by $A_{en} = 8 n_1 \pi \hbar$, $S_{en} = 2\pi n_1\hbar$, are equally spaced accurately. (ii) However, near outer cosmological horizon the spectrums, which are in the form of $A_{cn} = 16 n_2 \pi \hbar - \sqrt{\frac{48\pi}{\Lambda}A_{cn} - 3 A_{cn}^2}$, $S_{cn} = 4 \pi n_2 \hbar - \sqrt{\frac{3\pi}{\Lambda}A_{cn} - 3/16 A_{cn}^2}$, are not markedly equidistant. Finally, we also discuss the electrically charged case and find the black holes in de Sitter spacetime have similar quantization behavior no matter with or without charge.