Holographic Entanglement Entropy as a Probe of Dynamical Criticality in Scalarizing Black Holes

TL;DR

This paper shows that holographic entanglement entropy can effectively detect both static and dynamical critical phenomena in black hole models, especially capturing the relaxation dynamics near critical points.

Contribution

It introduces the novel use of HEE to probe dynamical criticality and the flip phenomenon in scalarized black holes, linking HEE relaxation to scalar field dynamics.

Findings

HEE detects dynamical critical phenomena in black hole models.

HEE relaxation times scale logarithmically with distance from criticality.

HEE closely mirrors scalar field relaxation near the flip phenomenon.

Abstract

We demonstrate that holographic entanglement entropy (HEE) serves as a powerful diagnostic tool for both static and dynamical critical phenomena in the Einstein-Born-Infeld-Scalar (EBIS) model. While HEE is well-known for capturing static phase transitions, we reveal its novel ability to probe dynamical criticality, particularly the ''flip'' phenomenon-a sign inversion in the scalar field at a critical point. Near the flip, HEE exhibits relaxation dynamics that closely mirror those of the scalar field, with both relaxation times scaling logarithmically with the distance from the critical point. This intimate connection between the relaxation of HEE and the scalar field highlights HEE as a sensitive probe of dynamical critical phenomena. Our findings provide new insights into the interplay between quantum information and gravitational dynamics, offering a deeper understanding of critical behavior in strongly coupled systems.