Entropy in Spin Foam Models: The Statistical Calculation

TL;DR

This paper explores black hole entropy in spin foam models, comparing horizon-based and statistical mechanics approaches, demonstrating their interrelation and validity in the context of the BTZ black hole.

Contribution

It advances the understanding of black hole entropy calculation in spin foam models by linking horizon observables with statistical mechanics methods.

Findings

Both methods yield consistent entropy values.

Observables at the horizon are crucial for entropy calculations.

The approaches are theoretically interconnected.

Abstract

Recently an idea for computing the entropy of black holes in the spin foam formalism has been introduced. Particularly complete calculations for the three dimensional euclidean BTZ black hole were done. The whole calculation is based on observables living at the horizon of the black hole universe. Departing from this idea of observables living at the horizon, we now go further and compute the entropy of BTZ black hole in the spirit of statistical mechanics. We compare both calculations and show that they are very interrelated and equally valid. This latter behaviour is certainly due to the importance of the observables.