The first laws of thermodynamics of the (2+1)-dimensional BTZ black holes and Kerr-de Sitter spacetimes

TL;DR

This paper extends the first law of thermodynamics to (2+1)-dimensional BTZ black holes and Kerr-de Sitter spacetimes, showing that variable cosmological constant allows consistent mass formulas across different backgrounds.

Contribution

It demonstrates the extension of black hole thermodynamic laws to rotating black holes in anti-de Sitter and de Sitter spaces with variable cosmological constant.

Findings

Mass formulas are valid in asymptotic flat, anti-de Sitter, and de Sitter spacetimes.

Variable cosmological constant is crucial for extending the first law.

Formulas are applicable in any number of dimensions.

Abstract

We investigate the first law of thermodynamics in the case of the (2+1)-dimensional BTZ black holes and Kerr-de Sitter spacetimes, in particular, we focus on the integral mass formulas. It is found that by assuming the cosmological constant as a variable state parameter, both the differential and integral mass formulas of the first law of black hole thermodynamics in the asymptotic flat spacetimes can be directly extended to those of rotating black holes in anti-de Sitter and de Sitter backgrounds. It should be pointed that these formulas come into existence in any dimensions also.