The Cardy-Verlinde Formula and Charged Topological AdS Black Holes

TL;DR

This paper explores the relationship between the dynamics of a brane universe in charged topological AdS black hole backgrounds and the thermodynamics of the dual conformal field theory, deriving a generalized Cardy-Verlinde formula.

Contribution

It derives a generalized Cardy-Verlinde formula for CFTs with R-charge in the context of charged topological AdS black holes, linking Friedmann equations with thermodynamics.

Findings

Friedmann equations match CFT thermodynamics at black hole horizon crossing

Temperature and entropy relate to Hubble parameter and its derivative

Generalized Cardy-Verlinde formula obtained for any curvature parameter k

Abstract

We consider the brane universe in the bulk background of the charged topological AdS black holes. The evolution of the brane universe is described by the Friedmann equations for a flat or an open FRW-universe containing radiation and stiff matter. We find that the temperature and entropy of the dual CFT are simply expressed in terms of the Hubble parameter and its time derivative, and the Friedmann equations coincide with thermodynamic formulas of the dual CFT at the moment when the brane crosses the black hole horizon. We obtain the generalized Cardy-Verlinde formula for the CFT with an R-charge, for any values of the curvature parameter k in the Friedmann equations.