Phase transitions for the topological de Sitter spaces and Schwarzschild–de Sitter black hole

AbstractWe study whether the Hawking–Page phase transition may occur in topological de Sitter spaces (TdS) and Schwarzschild–de Sitter black hole (SdS). We show that at the critical temperature T=T1, TdS with hyperbolic cosmological horizon can make the Hawking–Page transition from the zero mass de Sitter space to TdS. It is also shown that there is no Hawking–Page transition for TdS with Ricci-flat and spherical horizons, when the zero mass de Sitter space is taken as the thermal background. Also we find that the SdS undergoes a different phase transition at T=0 which the Nariai black hole is formed. Finally we connect our results to the dS/CFT correspondence