Holography and Brane Cosmology in Domain Wall Backgrounds

TL;DR

This paper explores the holographic relationship between domain-wall black holes and quantum field theories, deriving cosmological equations and entropy relations that connect black hole physics with brane universe dynamics.

Contribution

It introduces a new class of domain-wall black hole solutions and establishes a correspondence with brane cosmology, including a Cardy-Verlinde-like entropy formula.

Findings

The brane's equation of motion maps to FRW equations with a varying gravitational constant.

A Cardy-Verlinde-like entropy formula is derived for the QFT.

The entropy of domain-wall black holes saturates the Hubble entropy bound at the horizon crossing.

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.