Dynamical probe of thermodynamical properties in three-dimensional hairy AdS black holes

TL;DR

This paper demonstrates that quasinormal modes of electromagnetic perturbations can dynamically probe the thermodynamic stability and phase transitions of three-dimensional hairy AdS black holes in both Jordan and Einstein frames.

Contribution

It shows that QNM frequencies reflect thermodynamic stability and phase transitions in hairy AdS black holes, providing a dynamic method to study black hole thermodynamics.

Findings

Imaginary parts of QNM frequencies indicate thermodynamical stability.

QNM analysis reveals phase transitions between hairy black holes and BTZ black holes.

Results are consistent in both Jordan and Einstein frames.

Abstract

We study separatively the quasinormal modes (QNM) of electromagnetic perturbations around three-dimensional anti-de Sitter(AdS) black holes in Jordan and Einstein frames, which are related by the conformal transformations and a redefinition of a scalar field. We find that, in the Jordan frame, the imaginary parts of QNM frequencies can reflect the thermodynamical stabilities of hairy black holes, including the possible phase transition between the hairy black hole and BTZ black hole, disclosed by examining the corresponding free energies. Similar results are also uncovered in the Einstein frame. The obtained results further support that the QNM can be a dynamic probe of the thermodynamic properties in black holes.