Cardy-Verlinde formula and AdS black holes - art. no. 124018

In a recent paper by E. Verlinde, hep-th/0008140, an interesting formula ha s been put forward, which relates the entropy of a conformal formal field i n arbitrary dimensions to its total energy and Casimir energy. This formula has been shown to hold for the conformal field theories that have anti-de Sitter (AdS) duals in the cases of AdS Schwarzschild black holes and AdS Ke rr black holes. In this paper we further check this formula with various bl ack holes with AdS asymptotics. For the hyperbolic AdS black holes, the Car dy-Verlinde formula is found to hold if we choose the "massless" black hole as the ground state, but in this case, the Casimir energy is negative. For the AdS Reissner-Nordstrom black holes in arbitrary dimensions and charged black holes in D = 5, D = 4, and D = 7 maximally supersymmetric gauged sup ergravities, the Cardy-Verlinde formula holds as well, but a proper interna l energy, which corresponds to the mass of supersymmetric backgrounds, must be subtracted from the total energy. We fail to rewrite the entropy of cor responding conformal field theories in terms of the Cardy-Verlinde formula for the AdS black holes in Lovelock gravity.