Entanglement Entropy, Phase Transition, and Island Rule for Reissner-Nordstr\"om-AdS Black Holes

TL;DR

This paper investigates how phase transitions in Reissner-Nordström-AdS black holes affect entanglement entropy and the Page curve, revealing new phenomena and confirming unitarity despite morphological changes.

Contribution

It explores the impact of first-order phase transitions on the Page curve in black hole evaporation, a previously unexamined aspect.

Findings

Entanglement entropy follows the Page curve pattern with linear growth and eventual plateau.

Phase transitions alter the shape of the Page curve but do not violate unitarity.

Diverse Page curve configurations emerge during black hole evaporation, indicating novel phenomena.

Abstract

This study focuses on the examination of the island rule within the context of four-dimensional Reissner-Nordstr\"om-AdS (4D RN-AdS) black holes, illuminating the intricate relationship between the entanglement entropy and phase transitions of black holes. The entanglement entropy of 4D RN-AdS black holes follows the anticipated linear growth pattern before ultimately declining to a constant value, in accordance with the well-established Page curve. The novelty of this study lies in the examination of the influence, previously unexplored, of the first-order phase transition on the shape and evolution of the Page curve in situations involving both eternal and evaporating black holes. Despite the morphological alterations of the curve induced by the transition, the inherent unitarity of the system persists. As the evaporation progresses, the Page curve displays diverse configurations, unveiling phenomena that are novel and defies traditional expectations, thereby enriching our comprehension of the thermodynamics of black holes interlinked with quantum information.