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

TL;DR

The work tackles how to describe the thermodynamics of black holes in de Sitter spaces within a holographic framework. It shows that cosmological horizon entropy can be cast into the Cardy-Verlinde form when using BBM boundary masses, and that black hole horizon entropy can be similarly cast when using Abbott-Deser charges, across SdS, RNdS, and Kerr-dS. The results imply a dual-CFT description for each horizon, though with nonunitary aspects in de Sitter/CFT and a need for separate CFTs for the cosmological and black hole horizons. The paper also derives the first laws of de Sitter black hole mechanics and discusses their physical interpretation and implications for dS/CFT and holography.

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-Nordström-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.