The Cardy-Verlinde Formula and Topological AdS-Schwarzschild Black Holes

TL;DR

This paper explores the relationship between the Cardy-Verlinde formula and topological AdS-Schwarzschild black holes, deriving a modified entropy formula applicable to various curvature parameters in brane cosmology.

Contribution

It introduces a modified Cardy-Verlinde formula that applies to brane universes with different spatial curvatures in the context of topological AdS-Schwarzschild black holes.

Findings

Expressed temperature and entropy in terms of Hubble parameter at black hole horizon crossing

Proposed a generalized Cardy-Verlinde formula valid for any curvature parameter k

Connected black hole thermodynamics with brane universe cosmology

Abstract

We consider the brane universe in the background of the topological AdS-Schwarzschild 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 closed 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-Verlinde formula which is valid for any values of the curvature parameter k in the Friedmann equations.