BTZ Black Hole Entropy from Ponzano-Regge Gravity

TL;DR

This paper calculates the entropy of the BTZ black hole using Ponzano-Regge lattice gravity, showing that all triangulations of the Euclidean black hole reproduce the expected semi-classical entropy behavior.

Contribution

It demonstrates that the BTZ black hole entropy can be derived from all possible triangulations within the Ponzano-Regge framework, linking quantum geometry to classical entropy.

Findings

Reproduces semi-classical entropy behavior

All triangulations contribute to entropy calculation

Validates Ponzano-Regge approach for black hole entropy

Abstract

The entropy of the BTZ black hole is computed in the Ponzano-Regge formulation of three-dimensional lattice gravity. It is seen that the correct semi-classical behaviour of entropy is reproduced by states that correspond to all possible triangulations of the Euclidean black hole.