d-Dimensional Black Hole Entropy Spectrum from Quasi-Normal Modes

Gabor Kunstatter

doi:10.1103/PhysRevLett.90.161301

paper

d-Dimensional Black Hole Entropy Spectrum from Quasi-Normal Modes

arXiv:gr-qc/0212014 · doi:10.1103/PhysRevLett.90.161301

Abstract

Starting from recent observations\cite{hod,dreyer1} about quasi-normal modes, we use semi-classical arguments to derive the Bekenstein-Hawking entropy spectrum for $d$ -dimensional spherically symmetric black holes. We find that the entropy spectrum is equally spaced: $S_{B H} = k ln (m_{0}) n$ , where $m_{0}$ is a fixed integer that must be derived from the microscopic theory. As shown in \cite{dreyer1},4- $d$ loop quantum gravity yields precisely such a spectrum with $m_{0} = 3$ providing the Immirzi parameter is chosen appropriately. For $d$ -dimensional black holes of radius $R_{H} (M)$ , our analysis requires the existence of a unique quasinormal mode frequency in the large damping limit $ω^{(d)} (M) = α^{(d)} c / R_{H} (M)$ with coefficient $α^{(d)} = (d - 3) / o v er 4 π ln (m_{0})$ , where $m_{0}$ is an integer and $Γ^{(d - 2)}$ is the volume of the unit $d - 2$ sphere.

4 pages, Latex, Revtex4 Some formulas corrected, a reference added

d-Dimensional Black Hole Entropy Spectrum from Quasi-Normal Modes

Abstract

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