De Sitter space versus Nariai Black Hole: stability in d5 higher derivative gravity

TL;DR

This paper investigates the stability of Nariai black holes in five-dimensional higher derivative gravity, revealing conditions where they are stable, contrasting with Einstein gravity, and exploring implications for dS/CFT correspondence.

Contribution

It demonstrates the existence of stable Nariai black holes in d5 higher derivative gravity, unlike in Einstein gravity, and discusses potential dual CFT phase interpretations.

Findings

Nariai black holes can be stable in d5 higher derivative gravity.

Pure de Sitter space remains stable in Einstein gravity, but not necessarily in higher derivative theories.

Implications for dual CFT phases in dS/CFT correspondence are proposed.

Abstract

d5 higher derivative gravity on the Schwarzschild-de Sitter (SdS) black hole background is considered. Two horizons SdS BHs are not in thermal equilibrium and Hawking-Page phase transitions are not expected there, unlike to the case of AdS BHs. It is demonstrated that there exists the regime of d5 theory where Nariai BH which is extremal limit of SdS BH is stable. It is in the contrast with Einstein gravity on such backgroundwhere only pure de Sitter space is always stable. Speculating on the applications in proposed dS/CFT correspondence, these two (de Sitter and Nariai) stable spaces may correspond to confining-deconfining phases in dual CFT.