Cardy-Verlinde Formula and Kerr-Newman-AdS4 and two rotation parameters Kerr-AdS5 black holes

The Cardy-Verlinde formula, which expresses the entropy of the conformal field theory in terms of its total energy (or the extensive energy), Casimir energy and radius of the unit sphere S, is further verified by using the Kerr-Newman-AdS4 and the two rotation parameters Kerr-AdS5 black holes. For the Kerr-Newman-AdS4 black hole we find that to cast the entropy of the conformal field theory into the Cardy-Verlinde formula the energies n ( JΩH + QΦ 2 + QΦ0 2 ) , which relate to rotational and electric potential energies, must be subtracted from the Casimir energy, and the electric potential energy QΦ0 2 from the total energy. On the other hand, we show that for the two parameters Kerr-AdS5 black hole the standard Cardy-Verlinde formula holds if we subtract the rotation energy n ∑ i JiΩi from the Casimir energy. The result for the case of the Kerr-AdS5 black hole may be extended to higher dimensional Kerr-AdS black holes with multi-rotation-parameters since it is valid for the Kerr-AdSn black holes with one or two rotation parameters. PACS numbers: 04.70.Dy, 04.20.-q, 97.60.Lf. Typeset using REVTEX email: [email protected]