Dynamical perturbations and critical phenomena in Gauss-Bonnet-AdS black holes

TL;DR

This paper studies how high curvature effects in 5D Gauss-Bonnet AdS black holes influence scalar field perturbations and phase transitions, revealing that critical exponents remain mean-field despite curvature effects.

Contribution

It provides new insights into the impact of Gauss-Bonnet terms on black hole perturbations and critical phenomena, showing no change in critical exponents.

Findings

High curvature affects scalar perturbations and condensation.

Critical exponents remain mean-field despite curvature effects.

Linear response functions reflect high curvature influences.

Abstract

We investigate the perturbations of charged scalar field in $5$-dimensional Gauss-Bonnet AdS black hole backgrounds. From the perturbation behaviors we obtain the objective picture on how the high curvature influence the spacetime perturbation and the condensation of the scalar hair. The high curvature effects can also be read from the linear response function such as the susceptibility and the correlation length, when the system approaches the critical point. We find that the Gauss-Bonnet term does not affect the critical exponents of the system and they still take the mean-field values.