De Sitter space versus Nariai black hole: stability in D5 higher derivative gravity

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 background where 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.