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

Abstract

In the background of a charged AdS dilaton black hole, we investigate the movement of a selfgraviting 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 = 1 3 ρ) should be given. According to the holographic renormalization procedure, we involve an appropriate surface counterterm into the gravitational action for achieving P = 1 3 ρ 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.

Holographic complexity growth for a charged AdS-dilaton black holes with fixed and dynamical boundary respectively

“…For getting a finite mass of black hole, we need to find a well-defined quasilocal stress-energy T tt . Thus, we choose the undetermined coefficients in (17) as [45]. After substitute these coefficients and ( 11)-( 15) into (22), the expression of black hole mass is obtained as…”

“…where we have used the (42). In brief, (45) means that the complexity growth rate, especially in the late time limit, can not exceed the bound 8πM √ 3 , whatever how large the dilaton coupling α is.…”

“…In this part, we briefly review the movement of a selfgraviting 3-brane in charged AdS-dilaton black holes, one can refer [45] to get more detail. We assume M is a five-dimensional manifold containing a brane Σ with two sides, which splits M into two parts with a Z 2 symmetry.…”

“…Thus, it is worthwhile to explore the effects of dilaton coupling constant on the growth rate of holographic complexity. In comparison with the work [33], except to generalize their results from AdS-Schwarzschild black hole to charged AdS-dilaton black holes, we also consider the self-gravitating effects of brane by using the method provided in [45][46][47].…”

“…Besides, it has been indicated that the dilaton coupling constant play an important role in many phenomenological aspects of dilaton gravity. For example, the different phases structures of black hole thermodynamics is analyzed by [42,43] in different dilaton coupling constants; [44,45] observe the various evolution modes of brane universe as varying the value of dilaton coupling constant. Thus, it is worthwhile to explore the effects of dilaton coupling constant on the growth rate of holographic complexity.…”