Entanglement Islands, Page curves and Phase Transitions of Kerr-AdS Black Holes

TL;DR

This paper analyzes the entanglement entropy and Page curve of Kerr-AdS black holes using the island paradigm, revealing how phase transitions affect the entropy evolution while maintaining unitarity.

Contribution

It introduces the study of phase transition effects on the Page curve for Kerr-AdS black holes within the island framework, a novel aspect in black hole information research.

Findings

Page curve shows linear growth then saturation, consistent with unitarity.

First order phase transition causes a sharp discontinuity in the Page curve.

Entropy evolution remains consistent with quantum unitarity across scenarios.

Abstract

We study the Page curve and information paradox for Kerr AdS black hole in light of entanglement entropy by employing the recently proposed island paradigm. By incorporating the island rule, we show that the entanglement entropy of Kerr AdS black hole grows linearly at early times and declines to a constant value at late times in agreement with the well established Page curve. The novelty of this study resides in the investigation of influence of phase transitions on the page curve in two different ensembles. We find that a first order phase transition results in a sharp discontinuity in the Page curve. We study the evaporation process in different scenarios and find that in all the situations, the Page curve doesn't violate the unitary principle of quantum mechanics.