Quantum Entropy of Charged Rotating Black Holes

For more than two decades physicists have come to appreciate black holes as thermodynamic systems characterized by only a few macroscopic parameters such as mass (m), charge (q) and angular momentum (Ω). The generic representative of such a hole in general relativity is the Kerr-Newman metric . The thermodynamic analogy suggests that there is an entropy associated with this hole that is proportional to the area of the event horizon. For all other thermodynamic systems, the entropy is proportional to the logarithm of the number of hidden degrees of freedom. Are there analogous degrees of freedom are for a black hole? If so, where do they come from? Statistical explanations of their origin in terms of a gas of quantum fields have been proposed . Unfortunately the resultant expressions for the entropy can be understood as one-loop corrections to the classical black hole entropy, and so do not give any explanation of the classical entropy itself. For arbitrary static black holes, the divergences of the entropy have the same origin as the UV-divergences of the quantum effective action and can be removed by remormalization of the gravitational couplings in the treelevel gravitational action. I report here on work carried out with S. Solodukhin for the analogous problem in the stationary case. Remarkably, the UV-divergences for the one-loop entropy of a Kerr-Newman black hole are renormalized in the same way as for a static black hole.