Statistical description of the black hole degeneracy spectrum

TL;DR

This paper employs mathematical generating functions to analyze the statistical properties of black hole degeneracy spectra in loop quantum gravity, revealing the disappearance of entropy quantization at large areas.

Contribution

It introduces a mathematical approach to study black hole entropy spectra in loop quantum gravity, showing how quantization effects fade with increasing horizon area.

Findings

Entropy quantization persists at small areas

Quantization effects diminish as area increases

Method applicable to various black hole entropy proposals

Abstract

We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity.