(Anti–)de Sitter black holes in higher derivative gravity and dual conformal field theories

The thermodynamics of five-dimensional Schwarzschild anti–de Sitter (SAdS) and SdS black holes (BHs) in the particular model of higher derivative gravity is considered. The free energy, mass (thermodynamical energy) and entropy are evaluated. A parameter region exists where BH entropy is zero or negative. Arguments are given that the corresponding BH solutions are not stable. We also present the Friedmann-Robertson-Walker (FRW) equations of motion of time- (space-)like branes in SAdS or SdS BH backgrounds. The properties of dual conformal field theory (CFT) are discussed and it is shown that it has a zero Casimir energy when BH entropy (effective gravitational constant) is zero. The Cardy-Verlinde formula for CFT dual to a SAdS or SdS BH is found in a universal form.