EFFECTIVE 2-DIMENSIONAL DESCRIPTION FROM CRITICAL PHENOMENA IN BLACK-HOLES

We study the occurrence of critical phenomena in four-dimensional, rot ating and charged black holes, derive the critical exponents and show that they fulfill the scaling laws. Correlation function critical expo nents and Renormalization Group considerations assign an effective (sp atial) dimension, d = 2, to the system. The two-dimensional Gaussian a pproximation to critical systems is shown to reproduce all the black h ole's critical exponents. Higher order corrections (which are always r elevant) are discussed. Identifying the two-dimensional surface with t he event horizon and noting that generalization of scaling leads to co nformal invariance and then to string theory, we arrive at 't Hooft's string interpretation of black holes. From this, a model for dealing w ith 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 similar or equal to (1/root 2 )M(pl)root l with an l positive integer and then, from this result, to the proportionality between quantum entropy and area.