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

D5 higher derivative gravity on the Schwarzschild-de Sitter (SdS) black hol e background is considered. Two horizons SdS BHs are not in thermal equilib rium and Hawking-Page phase transitions are not expected there, unlike to t he case of AdS BHs. It is demonstrated that there exists the regime of D5 t heory 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 S itter space is always stable. Speculating on the applications in proposed d S/CFT correspondence, these two (de Sitter and Nariai) stable spaces may co rrespond to confining-deconfining phases in dual CFT. (C) 2001 Elsevier Sci ence B.V. All rights reserved.