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.
Highlights
The study about physics beyond four-dimensional (4D) spacetime has made great progress in recent decades; a lot of interesting physics was obtained from either the phenomenological aspects or theoretical implications, such as M theory [1,2], anti de–Sitter space/conformal field theory [3,4] (i.e., anti– de Sitter (AdS)=CFT) correspondence, and the brane world scenario in which our universe is viewed as a 3 þ 1 dimensional brane embedded in a higher-dimensional spacetime [5,6,7]
In our scenario, we involve the gravity on the brane by using the method provided in [13], and the evolution of brane is determined by the effective Einstein field equation on the brane and the Israel junction condition together
In the background of a charged AdS dilaton black hole solved by [47,48,49], we study the movement of a selfgraviting brane and holographic effects as the brane gets close to the AdS boundary
Summary
The study about physics beyond four-dimensional (4D) spacetime has made great progress in recent decades; a lot of interesting physics was obtained from either the phenomenological aspects or theoretical implications, such as M theory [1,2], anti de–Sitter space/conformal field theory [3,4] (i.e., AdS=CFT) correspondence, and the brane world scenario in which our universe is viewed as a 3 þ 1 dimensional brane embedded in a higher-dimensional spacetime [5,6,7]. By combining three different Liouville-type dilaton potentials, [47,48,49] obtain the asymptotically AdS black hole solution in EinsteinMaxwell-Dilaton theory Based on this black hole solution, many interesting physical phenomenologies have been explored, like the black hole thermodynamics [50,51], holographic thermalization [52], black hole phase transition in extend phase space [53], and domain wall cosmology [54]. When considering the motion of the domain wall in this charged AdS dilaton black hole, [54] observes enriched evolution modes of the domain wall universe as varying the value of the dilaton coupling constant It seems that there exists a connection between the thermodynamics of the AdS dilaton black hole in the bulk spacetime and the evolution of FLRW universe on the brane/wall.
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