Entropy of the three dimensional Schwarzschild-de Sitter black hole

TL;DR

This paper analyzes the entropy and thermodynamics of the three-dimensional Schwarzschild-de Sitter black hole, establishing a correspondence with a two-dimensional conformal field theory and discussing entropy bounds.

Contribution

It provides a precise calculation of the black hole mass, clarifies the relations between mass, entropy, and temperature, and establishes the SdS$_3$/CFT$_2$-correspondence using the Cardy formula.

Findings

Correctly computed the SdS$_3$ black hole mass.

Established the entropy-temperature-mass relations.

Applied the Cardy formula to confirm the CFT duality.

Abstract

We study the three dimensional Schwarzschild-de Sitter (SdS$_3$) black hole which corresponds essentially to a conical defect. We compute the mass of the SdS$_3$ black hole from the correct definition of the mass in asymptotically de Sitter space. Then we clarify the relation between the mass, entropy and temperature for this black hole without any ambiguity. Also we establish the SdS$_3$/CFT$_2$-correspondence for the entropy by applying the Cardy formula to a CFT with a central charge $c=3\ell/2G_3$. Finally we discuss the entropy bounds for the SdS$_3$ black hole.