Subregion Entropy for the Doubly Holographic Global Black String

TL;DR

This paper investigates how entanglement entropy evolves in a doubly holographic model of spherical AdS black holes, revealing new phase transition behaviors and geometric properties of entanglement surfaces.

Contribution

It introduces a new analysis of entanglement entropy growth in spherical black holes, highlighting the effects of an additional scale and uncovering novel critical phenomena.

Findings

Identification of a new critical black hole radius unrelated to thermodynamics

Distinct behavior of Ryu-Takayanagi surfaces in spherical versus planar cases

Analysis of the interplay between island formation and Hawking-Page transition

Abstract

We study the growth of entanglement entropy in a doubly holographic model of gravity for a spherical AdS black hole. Compared to previous work, which was limited to the case of planar black holes, this introduces an extra scale to the problem. This allows us to analyze the interplay between the reorganization of entanglement entropy due to island formation and the onset of the Hawking-Page phase transition and to find the appearance of a new critical black hole radius unrelated to the thermodynamics. We also find that the geometry of the Ryu-Takayanagi surface capturing the physics of islands exhibits drastically different behavior than in the planar case.