Black hole state degeneracy in Loop Quantum Gravity

TL;DR

This paper analyzes the combinatorial counting of black hole quantum states in Loop Quantum Gravity, explaining the origin of the degeneracy spectrum's band structure that leads to black hole entropy quantization, and derives analytical expressions for key quantities.

Contribution

It provides a qualitative understanding of the degeneracy spectrum's band structure and offers analytical formulas for related quantities in Loop Quantum Gravity.

Findings

Identifies the band structure as key to entropy quantization

Provides analytical expressions for degeneracy spectrum features

Clarifies the combinatorial origin of black hole state degeneracy

Abstract

The combinatorial problem of counting the black hole quantum states within the Isolated Horizon framework in Loop Quantum Gravity is analyzed. A qualitative understanding of the origin of the band structure shown by the degeneracy spectrum, which is responsible for the black hole entropy quantization, is reached. Even when motivated by simple considerations, this picture allows to obtain analytical expressions for the most relevant quantities associated to this effect.