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, $I=\int \frac{dE}{\omega (E)}$, 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 $A_n=2\pi \sqrt{\frac{nm\hslash }{\Lambda }}$ which is not equally spaced, in contrast with area spectrum of black hole in higher dimension.

arXiv comment7 pages, no figure, some refs added, clarifying comments added, no physics changed, version to appear in Class. Quant. Grav

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