Black hole entropy and quasi-normal modes

Starting from recent observations about quasi-normal modes, we use semi-classical arguments to derive the Bekenstein-Hawking entropy spectrum ford-dimensional spherically symmetric black holes.  We find that, as first suggested by Bekenstein, the entropy spectrum  is equally spaced: 

       S_BH = ln(m₀) n 

where m₀ is a fixed  integer that must be derived from the microscopic theory. For d-dimensional black holes of radius R_H(M), our analysis predicts the  form of the unique quasinormal mode frequency in the large damping limit. This prediction has  been confirmed by recent calculations. These developments indicate that the classical quasi-normal modes are providing crucial information about the quantum gravitational states responsible for black hole entropy.