The temperature and entropy of CFT on time-dependent backgrounds

TL;DR

This paper studies the temperature and entropy of a conformal field theory on time-dependent backgrounds by relating it to black hole configurations in AdS space, revealing how these thermodynamic quantities are affected by the boundary geometry.

Contribution

It provides a method to compute the stress-energy tensor, temperature, and entropy of the dual CFT on FLRW and dS backgrounds, highlighting the role of apparent horizons.

Findings

Entropy is proportional to the apparent horizon area.

Correctly reproduces the intrinsic temperature of de Sitter space.

Relates black hole thermodynamics to dual CFT on dynamic backgrounds.

Abstract

We express the AdS-Schwarzschild black-hole configuration in coordinates such that the boundary metric is of the FLRW type. We review how this construction can be used in order to calculate the stress-energy tensor of the dual CFT on the FLRW background. We deduce the temperature and entropy of the CFT, which are related to the temperature and entropy of the black hole. We find that the entropy is proportional to the area of an apparent horizon, different from the black-hole event horizon. For a dS boundary we reproduce correctly the intrinsic temperature of dS space.