Holographic Thermodynamic on the Brane in Topological Reissner-Nordstr\"om de Sitter Space

TL;DR

This paper explores the thermodynamics of a brane universe in a topological Reissner-Nordström de Sitter background, deriving formulas for entropy and energy that relate to the Hubble parameter and its derivatives.

Contribution

It derives a generalized Cardy-Verlinde formula for charged CFTs with a cosmological constant in a topological de Sitter setting, extending previous thermodynamic relations.

Findings

Thermodynamic quantities follow special forms at horizon crossings.

Derived a generalized Cardy-Verlinde formula for charged CFTs.

Results apply for any curvature parameter k.

Abstract

We consider the brane universe in the bulk background of the topological Reissner-Nordstr\"om de Sitter black holes. We show that the thermodynamic quantities (including entropy) of the dual CFT take usual special forms expressed in terms of Hubble parameter and its time derivative at the moment, when the brane crosses the black hole horizon or the cosmological horizon. We obtain the generalized Cardy-Verlinde formula for the CFT with an charge and cosmological constant, for any values of the curvature parameter $k$ in the Friedmann equations.