Brane universe and holography in spacetime of charged AdS dilaton black hole

TL;DR

This paper explores the holographic and cosmological implications of a brane moving near a charged AdS dilaton black hole, deriving an FLRW universe with radiation dominance and extending the Cardy-Verlinde formula.

Contribution

It introduces a method to incorporate surface counterterms for holographic renormalization and black hole mass calculation in charged AdS dilaton backgrounds.

Findings

Derived an exact FLRW metric on the brane near the AdS boundary.

Established a radiation-dominated universe with $P=\frac{1}{3}\rho$ via holography.

Extended the Cardy-Verlinde formula to this brane-world scenario.

Abstract

In the background of a charged AdS dilaton black hole, we investigate the movement of a self-graviting 3-brane and relevant holographic effects as the brane move close to the AdS boundary. The induced metric on brane corresponds to an exact FLRW geometry, while the evolution of brane is determined by Israel junction condition and the effective Einstein field equation on brane together. When the brane approaches the AdS boundary, AdS/CFT correspondence implies that a radiation dominated FLRW-universe ($P=\frac{1}{3}\rho$) should be given. According to the holographic renormalization procedure, we involve an appropriate surface counterterm into the gravitational action for achieving $P=\frac{1}{3}\rho$ on brane. This surface counterterm also plays a important role in caculating the mass of charged AdS dilaton black hole. Finally, we obtain the thermodynamic quantities and give an extend Cardy-Verlinde formula on brane.