Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting

TL;DR

This paper analyzes the conserved quantities and entropy of BTZ black holes, comparing geometric and Noether-based methods, and discusses their thermodynamic consistency and differences in entropy calculation approaches.

Contribution

It introduces a comprehensive framework for calculating BTZ black hole entropy and conserved quantities, comparing geometric and Wald methods.

Findings

Entropy computed satisfies the first law of thermodynamics.

Comparison shows differences between geometric and Wald entropy calculations.

Maximal extension of the BTZ horizon constructed for method comparison.

Abstract

The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription by Wald et al. we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.