Entanglement Temperature in Non-conformal Cases

TL;DR

This paper explores entanglement temperature in non-conformal holographic systems by generating analytical and numerical solutions for Einstein dilaton models, analyzing their thermal stability and thermodynamic laws.

Contribution

It introduces a numerical method for black hole solutions in Einstein dilaton systems and investigates their stability and thermodynamics in non-conformal backgrounds.

Findings

Black hole solutions are more thermally stable than thermal gas solutions.

Numerical methods successfully obtain black hole solutions with special dilaton potentials.

First law of thermodynamics holds in the entanglement system from holography.

Abstract

Potential reconstruction can be used to find various analytical asymptotical AdS solutions in Einstein dilation system generally. We have generated two simple solutions without physical singularity called zero temperature solutions. We also proposed a numerical way to obtain black hole solution in Einstein dilaton system with special dilaton potential. By using this method, we obtain the corresponding black hole solutions numerically and investigate the thermal stability of the black hole by comparing the free energy of thermal gas and the corresponding black hole. In two groups of non-conformal gravity solutions obtained in this paper, we find that the two thermal gas solutions are more unstable than black hole solutions respectively. Finally, we consider black hole solutions as a thermal state of zero temperature solutions to check that the first thermal dynamical law exists in entanglement system from holographic point of view.