2001/02/28 by Rong-Gen Cai · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1103/physrevd.63.124018
published as Phys.Rev. D63 (2001) 124018 · 18 pages, latex, no figures, discussions on the charged AdS black holes changed
arxiv created 2001/03/07 · openalex publication_date 2001/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper by E. Verlinde, hep-th/0008140, an interesting formula has been put forward, which relates the entropy of a conformal formal field in 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 Kerr black holes. In this paper we further check this formula with various black holes with AdS asymptotics. For the hyperbolic AdS black holes, the Cardy-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-Nordstr"om black holes in arbitrary dimensions and charged black holes in D=5, D=4, and D=7 maximally supersymmetric gauged supergravities, the Cardy-Verlinde formula holds as well, but a proper internal energy, which corresponds to the mass of supersymmetric backgrounds, must be subtracted from the total energy. We fail to rewrite the entropy of corresponding conformal field theories in terms of the Cardy-Verlinde formula for the AdS black holes in Lovelock gravity.