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Non-rotating BTZ black hole area spectrum from quasi-normal modes

M R Setare

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In this paper, by using the quasi-normal frequencies for a non-rotating BTZ black hole derived by Cardos and Lemos, also via Bohr–Sommerfeld quantization for an adiabatic invariant, I=\int {{\rm d}E\over \omega(E)} , where E is the energy of system and ω(E) is vibrational frequency, we are led to an equally spaced mass spectrum. The result for the area of the event horizon is A_{n}=2\pi \sqrt{\smash{\frac{nm \hbar}{\Lambda}}\vphantom{A^1}} which is not equally spaced, in contrast with the area spectrum of a black hole in higher dimension.


PACS

04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics

MSC

83C57 Black holes

Subjects

Gravitation and cosmology

Dates

Issue 6 (21 March 2004)

Received 13 August 2003

Published 23 February 2004



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