Time-evolution of holographic entanglement entropy and metric perturbations

TL;DR

This paper investigates how small, time-dependent deformations of Anti-de Sitter space affect holographic entanglement entropy, revealing that divergences remain unchanged while finite parts vary, and explores related thermodynamic properties.

Contribution

It provides a perturbative analysis of holographic entanglement entropy under time-dependent AdS deformations, highlighting the behavior of finite terms and entanglement temperature.

Findings

Divergent terms in entanglement entropy are unaffected by small deformations.

Finite terms of entanglement entropy change under perturbations.

Entanglement temperature is inversely proportional to the entangling region size.

Abstract

We study the holographic entanglement entropy under small deformations of AdS, including time-dependence. It is found through perturbative analysis that the divergent terms are not affected and the change appears only in the finite terms. We also consider the entanglement thermodynamic first law, and calculate the entanglement temperature and confirm that it is inversely proportional to the size of the entangling region.