Signature of the black hole phase transition in quasinormal modes

TL;DR

This paper investigates how strong interactions between scalar and Maxwell fields in charged AdS black holes and solitons reveal signatures of phase transitions through quasinormal mode behaviors, including the emergence of growing modes.

Contribution

It demonstrates the impact of strong scalar-Maxwell coupling on quasinormal modes, revealing phase transition signatures in charged AdS black holes and solitons.

Findings

Growing modes appear when scalar-Maxwell coupling is strong in charged AdS black holes.

A sudden change to growing modes signals phase transition signatures.

Magnetic charged AdS solitons do not exhibit scalar condensation or phase change.

Abstract

We study the perturbation of the scalar field interacting with the Maxwell field in the background of d-dimensional charged AdS black hole and AdS soliton. Different from the single classical field perturbation, which always has the decay mode in the black hole background, we observe the possible growing mode when the perturbation of the scalar field strongly couples to the Maxwell field. Our results disclose the signature of how the phase transition happens when the interaction among classical fields is strong. The sudden change of the perturbation to growing mode is also observed in the AdS soliton with electric potential. However in the magnetic charged AdS soliton background, we observe the consistent perturbation behavior when the interaction between scalar field and Maxwell field is considered. This implies that for the magnetic charged AdS soliton configuration, unlike the situation with electric potential, there is no scalar field condensation which causes the phase change.