The Emergence of an Effective two - dimensional Quantum Description from the study of Critical Phenomena in Black Holes

TL;DR

This paper explores critical phenomena in black holes, deriving an effective two-dimensional quantum description that links black hole thermodynamics, conformal invariance, and string theory, proposing a quantization model for black hole mass.

Contribution

It introduces a novel effective 2D quantum framework for black holes based on critical phenomena and scaling laws, connecting black hole physics with string theory and quantization.

Findings

Black holes exhibit critical exponents satisfying scaling laws.

An effective 2D description reproduces black hole critical exponents.

Proposes a quantization of black hole mass proportional to the Planck scale.

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 functions 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 to '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. $M\simeq{1\over\sqrt{2}}M_{pl} \sqrt{l}$ with a $l$ positive integer and then, from this result, to the proportionality between quantum entropy and area.