Effective two-dimensional description from critical phenomena in black holes

Abstract

We study the occurrence of critical phenomena in four-dimensional, rotating and charged black holes, derive the critical exponents and show that they fulfill the scaling laws. Correlation function critical exponents and Renormalization Group considerations assign an effective (spatial) dimension,d=2, to the system. The two-dimensional Gaussian approximation to critical systems is shown to reproduce all the black hole's critical exponents. Higher order corrections (which are always relevant) are discussed. Identifying the two-dimensional surface with the event horizon and noting that generalization of scaling leads to conformal invariance and then to string theory, we arrive at 't Hooft's string interpretation of black holes. From this, a model for dealing with a coarse grained black hole quantization is proposed. We also give simple arguments that lead to a rough quantization of the black hole mass in units of the Planck mass, i.e.M≃(1/√2)MPl√l with anl positive integer and then, from this result, to the proportionality between quantum entropy and area.