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

TL;DR

This paper investigates phase transitions in topological de Sitter spaces and Schwarzschild-de Sitter black holes, revealing conditions for Hawking-Page transitions and their implications for the dS/CFT correspondence.

Contribution

It identifies specific conditions under which Hawking-Page transitions occur in TdS and analyzes the phase transition in SdS leading to Nariai black holes.

Findings

Hawking-Page transition occurs at T=T1 for hyperbolic TdS.

No Hawking-Page transition for Ricci-flat and spherical TdS.

SdS undergoes a phase transition at T=0 forming Nariai black holes.

Abstract

We 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 $T=T_1$, 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.