Entropy of the three dimensional Schwarzschild-de Sitter black hole

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.