Phase transition and quasinormal modes for charged black holes in 4D Einstein-Gauss-Bonnet gravity

In four-dimensional Einstein-Gauss-Bonnet (EGB) gravity, we consider the thermodynamic and phase transitions of (charged) AdS black holes. For the negative GB coefficient, alpha< 0, the system allows two physical critical points, corresponding to the reentrant phase transition, when the charge Q > 2 root-alpha. For arbitrary alpha > 0, the system always leads to a van der Waals phase transition. We then study the quasinormal modes (QNMs) of massless scalar perturbations to probe the van der Waals-like phase transition between small and large black holes (SBH/LBH) for (charged) AdS black holes. We find that the signature of this SBH/LBH phase transition in the isobaric process can be detected since the slopes of the QNM frequencies change dramatically in small and large black holes near the critical point. The obtained results further support that QNMs can be a dynamic probe of thermo-dynamic properties in black holes.