# Entanglement growth during Van der Waals like phase transition

## TL;DR

This paper investigates entanglement growth during a Van der Waals-like phase transition between two black hole states in AdS space, highlighting continuous transition dynamics and implications for holography.

## Contribution

It introduces a model of black hole phase transition using Vaidya spacetime and analyzes entanglement evolution during the process.

## Key findings

- Entanglement grows continuously during the phase transition.
- Saturation time depends on the final black hole state.
- Transition preserves temperature and free energy of initial state.

## Abstract

We address the problem of describing the coexistence state of two different black holes and Van der Waals like phase transition in Reissner-Nordstr\"om-AdS space-time. We start by a small charged black hole, then introduce a collapsing neutral thin-shell described by Vaidya metric to form a large one. The formation of the large black hole does not change the temperature and free energy of the initial state. We discuss the entanglement growing during the phase transition. The transition is always continuous and the saturation time is determined by the final state. It opens a possibility for studying the holography from excited states to excited states.