Entanglement growth during Van der Waals like phase transition

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.