Holography and brane cosmology in domain wall backgrounds

Abstract

We consider a class of domain-wall black hole solutions in the dilaton gravity with a Liouville-type dilaton potential. Using the surface counterterm approach we calculate the stress-energy tensor of quantum field theory (QFT) corresponding to the domain-wall black hole in the domain-wall/QFT correspondence. A brane universe is investigated in the domain-wall black hole background. When the tension term of the brane is equal to the surface counterterm, we find that the equation of motion of the brane can be mapped to the standard form of FRW equations, but with a varying gravitational constant on the brane. A Cardy-Verlinde-like formula is found, which relates the entropy density of the QFT to its energy density. At the moment when the brane crosses the black hole horizon of the background, the Cardy-Verlinde-like formula coincides with the Friedmann equation of the brane universe, and the Hubble entropy bound is saturated by the entropy of domain-wall black holes. *

Nonasymptotically AdS/dS solutions and their higher dimensional origins

“…Klemm in [19] found supersymmetric solution in the four dimensional gauged N = 4, SU (2)×SU (2) supergarvity; Refs. [14,20,22,23] investigated domain wall solutions with k = 0 in Einstein-dilaton theory with a Liouville-type potential; Cvetic et al in [21] found a domain wall solution with k = 0 in an Einstein-Maxwell-dilaton theory with special coupling parameters a = b = 2/p in (2.27); for more recent discussions on the non-asymptotically AdS/dS solutions with k = 1 in four dimensional Einstein-Maxwell-dilaton theory without dilaton potential see [24,25]; other related discussions see [28].…”

“…Indeed, in the literature, for example, see Refs. [15]- [23], some exact solutions of the action (1.4) have been found in some special cases. These solution are asymptotically neither AdS nor dS, different from those (1.2) which are asymptotically AdS or dS.…”

“…Namely we have to take a positive cosmological constant Λ 0 in (2.22). Upon lifting, we obtain 23) Redefining r N (D−2)/N → r and rescaling the coordinates and the integration constant M, the solution can be rewritten as 24) where …”

“…These solution are asymptotically neither AdS nor dS, different from those (1.2) which are asymptotically AdS or dS. We have studied some aspects [14,22,23] of dual field theory to these gravity solutions in the spirit of holography, as the non-conformal generalizations of AdS-CFT correspondence and dS-CFT correspondence. Note that an action like (1.4) can also be obtained by dimensionally reducing Einstein-Maxwell theory with a cosmological constant to a lower dimension.…”

Heat engines for dilatonic Born–Infeld black holes

“…Non-asymptotically flat/AdS black hole space-times have been actively studied for possible extensions of holography [82][83][84][85][86][87][88][89][90][91][92][93][94][95][96]. The usual notions of thermodynamic mass, thought of as enthalpy of a space-time, akin to an AdS black hole go through for more general backgrounds.…”