# Behavior of quasinormal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity

## TL;DR

This paper investigates how quasinormal modes of scalar perturbations can signal Van der Waals-like phase transitions between small and large charged AdS black holes in massive gravity, demonstrating QNMs as effective probes.

## Contribution

It introduces the use of QNMs to detect thermodynamic phase transitions in charged AdS black holes within massive gravity, highlighting their potential as diagnostic tools.

## Key findings

- QNMs signal the SBH/LBH phase transition in isobaric and isothermal processes
- QNM behavior correlates with thermodynamic phase changes
- Supports QNMs as tools for studying black hole thermodynamics

## Abstract

In this work, we utilize the quasinormal modes (QNMs) of a massless scalar perturbation to probe the Van der Waals-like small and large black holes (SBH/LBH) phase transition of charged topological Anti-de Sitter (AdS) black holes in four-dimensional massive gravity. We find that the signature of this SBH/LBH phase transition is detected in the isobaric as well as in the isothermal process.This further supports the idea that the QNMs can be an efficient tool to investigate the thermodynamical phase transition.