Universality of quantum entropy for extreme black holes
Abstract
We consider the extremal limit of a black hole geometry of the ReissnerNordstrom type and compute the quantum corrections to its entropy. Universally, the limiting geometry is the direct product of two 2dimensional spaces and is characterized by just a few parameters. We argue that the quantum corrections to the entropy of such extremal black holes due to a massless scalar field have a universal behavior. We obtain explicitly the form of the quantum entropy in this extremal limit as a function of the parameters of the limiting geometry. We generalize these results to black holes with toroidal or higher genus horizon topologies. In general, the extreme quantum entropy is completely determined by the spectral geometry of the horizon and in the ultraextreme case it is just a determinant of the 2dimensional Laplacian. As a byproduct of our considerations we obtain expressions for the quantum entropy of black holes which are not of the ReissnerNordstrom type: the extreme dilaton and extreme KerrNewman black holes. In both cases the classical BekensteinHawking entropy is modified by logarithmic corrections.
 Publication:

Nuclear Physics B
 Pub Date:
 July 1998
 DOI:
 10.1016/S05503213(98)000947
 arXiv:
 arXiv:hepth/9709064
 Bibcode:
 1998NuPhB.523..293M
 Keywords:

 QUANTUM ENTROPY;
 EXTREME BLACK HOLE;
 QUANTUM FIELDS;
 QUANTUM GRAVITY;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 18 pages, latex, no figures, minor changes, to appear in Nucl. Phys. B