d-Dimensional Black Hole Entropy Spectrum from Quasinormal Modes

Starting from recent observations about quasinormal modes, we use semiclassical arguments to derive the Bekenstein-Hawking entropy spectrum for d-dimensional spherically symmetric black holes. We find that, as first suggested by Bekenstein, the entropy spectrum is equally spaced: S_BH=kln⁡(m₀)n, where m₀ is a fixed integer that must be derived from the microscopic theory. As shown in O. Dreyer, gr-qc/0211076, 4D loop quantum gravity yields precisely such a spectrum with m₀=3 providing the Immirzi parameter is chosen appropriately. For d-dimensional black holes of radius R_H(M), our analysis predicts 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)/4πln⁡(m₀), where m₀ is an integer.