The Cardy-Verlinde formula and topological AdS-Schwarzschild black holes

We consider the brane universe in the back-round of the topological AdS-Sch warzschild black holes. The induced geometry of the brane is that of a flat or an open radiation dominated FRW-universe. Just like the case of a close d radiation dominated FRW-universe, the temperature and entropy are simply expressed in terms of the Hubble parameter and its time derivative when the brane crosses the black hole horizon. We propose the modified Cardy-Verlin de formula which is valid for any values of the curvature parameter k in th e Friedmann equations. (C) 2001 Elsevier Science B.V. All rights reserved.