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

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.

💡 Research Summary

This paper addresses the information‑paradox problem for rotating Kerr‑AdS black holes by applying the recently developed entanglement‑island prescription. The authors first review the Kerr‑AdS metric and perform a near‑horizon dimensional reduction, showing that a massless scalar field in the four‑dimensional background can be described by an effective two‑dimensional theory coupled to a dilaton and a U(1) gauge field. Using tortoise and Kruskal coordinates they rewrite the reduced metric in a conformally flat form, which allows them to treat Hawking radiation as a two‑dimensional conformal field theory (CFT) with central charge c.

The entanglement entropy of the Hawking radiation is computed in two scenarios. Without an island, the entropy of the radiation region R (bounded by points b⁺ and b⁻) is \