Holographic Entropy on the Brane in de Sitter Schwarzschild Space

TL;DR

This paper explores the relationship between the entropy of de Sitter Schwarzschild space and the dual CFT on the brane, demonstrating exact entropy matching at the horizon crossing, extending holographic principles beyond AdS spaces.

Contribution

It shows that the entropy correspondence holds for branes in de Sitter Schwarzschild space, including cases with different brane metrics, and relates to the AdS/CFT framework.

Findings

Entropy of CFT matches black hole entropy at horizon crossing

Cosmological constant effects depend on brane metric choice

Holographic entropy relation extends to de Sitter backgrounds

Abstract

The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both for time-like and space-like cases, the entropy of the CFT exactly agrees with the black hole entropy of 5-dimensional AdS Schwarzschild background as it happens in the AdS/CFT correspondence.