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(m(0))n, where m(0) 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 m(0)=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 omega((d))(M)=alpha((d))c/R-H(M) with coefficient alpha((d))=(d-3)4piln(m(0)), where m(0) is an integer.