Non-Rotating BTZ Black Hole Area Spectrum from Quasi-normal Modes

Abstract

In this paper, by using the quasi-normal frequencies for non-rotating BTZ black hole derived by Cardos and Lemos, also via Bohr-Sommerfeld quantization for an adiabatic invariant, $I=\int {dE\over \omega(E)}$, which $E$ is the energy of system and $\omega(E)$ is vibrational frequency, we leads to an equally spaced mass spectrum. The result for the area of event horizon is $A_{n}=2\pi \sqrt{\frac{nm \hbar}{\Lambda}}$ which is not equally spaced, in contrast with area spectrum of black hole in higher dimension.