Notes on solution phase space and BTZ black hole

TL;DR

This paper employs the covariant phase space formalism to compute conserved charges of the BTZ black hole, analyze its thermodynamics, and extend the analysis to Kerr-dS spacetime, providing detailed results for future research.

Contribution

It applies the solution phase space approach to BTZ and Kerr-dS black holes, offering detailed calculations of conserved charges and thermodynamic relations.

Findings

Conserved charges for BTZ black hole computed.

First law and Smarr relation confirmed for BTZ.

Results consistent with previous studies.

Abstract

In this paper, we use the solution phase space approach based on the covariant phase space formalism to compute the conserved charges of the BTZ black hole, namely mass, angular momentum, and entropy. Furthermore, we discuss the first law of the BTZ black hole and the Smarr relation. For completeness, outer horizon and inner horizon cases have been all included. Additionally, the results of the three-dimensional Kerr-dS spacetime have also been obtained. Our results are consistent with previous investigations. Considering the simplicity of the circumstances, we have presented the most detailed possible information, with the aim of facilitating research in related fields.