Universality of Quantum Entropy for Extreme Black Holes

TL;DR

This paper investigates the universal behavior of quantum entropy corrections for extremal black holes, showing they depend on horizon geometry and are applicable to various black hole types, including dilaton and Kerr-Newman.

Contribution

It demonstrates the universality of quantum entropy corrections for extremal black holes and provides explicit formulas based on horizon spectral geometry, extending to diverse black hole solutions.

Findings

Quantum corrections are universal and depend on horizon geometry.

Explicit entropy formulas involve determinants of the Laplacian.

Results apply to Reissner-Nordstrom, dilaton, and Kerr-Newman black holes.

Abstract

We consider the extremal limit of a black hole geometry of the Reissner-Nordstrom type and compute the quantum corrections to its entropy. Universally, the limiting geometry is the direct product of two 2-dimensional 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 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 ultra-extreme case it is just a determinant of the 2-dimensional Laplacian. As a byproduct of our considerations we obtain expressions for the quantum entropy of black holes which are not of the Reissner-Nordstrom type: the extreme dilaton and extreme Kerr-Newman black holes. In both cases the classical Bekenstein-Hawking entropy is modified by logarithmic corrections.