Cardy-Verlinde Formula and Thermodynamics of Black Holes in de Sitter Spaces

TL;DR

This paper extends the application of the Cardy-Verlinde formula to black hole horizons in de Sitter spaces, showing that their entropy can be expressed in this form using Abbott-Deser conserved charges, and discusses related thermodynamic laws.

Contribution

The paper generalizes previous results to Reissner-Nordström-de Sitter and Kerr-de Sitter black holes, demonstrating the entropy can be written in the Cardy-Verlinde form with Abbott-Deser charges.

Findings

Black hole entropy in de Sitter space can be expressed via the Cardy-Verlinde formula.

The Abbott-Deser definition of conserved charges is crucial for this formulation.

The first law of de Sitter black hole mechanics is established.

Abstract

We continue the study of thermodynamics of black holes in de Sitter spaces. In a previous paper (hep-th/0111093), we have shown that the entropy of cosmological horizon in the Schwarzschild-de Sitter solution and topological de Sitter solution can be expressed in a form of the Cardy-Verlinde formula, if one adopts the prescription to compute the gravitational mass from data at early or late time infinity of de Sitter space. However, this definition of gravitational mass cannot give a similar expression like the Cardy-Verlinde formula for the entropy associated with the horizon of black holes in de Sitter spaces. In this paper, we first generalize the previous discussion to the case of Reissner-Nordstr\"om-de Sitter and Kerr-de Sitter solutions. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. We discuss the implication of our result. In addition, we give the first law of de Sitter black hole mechanics.