Conserved Charges and First Law of Thermodynamics for Kerr-de Sitter Black Holes

TL;DR

This paper applies a new method to compute conserved charges and derive the first law of thermodynamics for Kerr-de Sitter black holes, unifying their thermodynamics across different asymptotic geometries and extending to charged solutions.

Contribution

It introduces the solution phase space method for calculating conserved charges and thermodynamics of Kerr-dS black holes, including charged cases, in a unified framework.

Findings

Calculated mass and angular momentum for Kerr-dS black holes.

Derived entropy and first law of thermodynamics for horizons.

Extended analysis to Kerr-Newman-dS black holes with electric charge.

Abstract

Recently, a general method for calculating conserved charges for (black hole) solutions to generally covariant gravitational theories, in any dimensions and with arbitrary asymptotic behaviors has been introduced. Equipped with this method, which can be dubbed as "solution phase space method," we calculate mass and angular momentum for the Kerr-dS black holes. Furthermore, for any choice of horizons, associated entropy and the first law of thermodynamics are derived. Interestingly, according to insensitivity of the analysis to the chosen cosmological constant, the analysis unifies the thermodynamics of rotating stationary black holes in 4 (and other) dimensions with either AdS, flat or dS asymptotics. We extend the analysis to include electric charge, i.e. to the Kerr-Newman-dS black holes.