Holographic Entanglement Entropy at Finite Temperature

TL;DR

This paper investigates how holographic entanglement entropy behaves in various black hole and brane backgrounds at finite temperature, exploring its potential to signal phase transitions.

Contribution

It provides a systematic analysis of entanglement entropy in multiple supergravity geometries with horizons, highlighting the absence of phase transition signals.

Findings

Entanglement entropy generally does not show a transition in studied backgrounds.

One configuration always dominates the entanglement entropy.

The study enhances understanding of holographic entanglement at finite temperature.

Abstract

Using a holographic proposal for the entanglement entropy we study its behavior in various supergravity backgrounds. We are particularly interested in the possibility of using the entanglement entropy as way to detect transitions induced by the presence horizons. We consider several geometries with horizons: the black hole in $AdS_3$, nonextremal Dp-branes, dyonic black holes asymptotically to $AdS_4$ and also Schwarzschild black holes in global $AdS_p$ coordinates. Generically, we find that the entanglement entropy does not exhibit a transition, that is, one of the two possible configurations always dominates.