Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane

TL;DR

This paper presents a holographic brane world model that analytically explores quantum extremal islands and the Page curve in black holes across various dimensions, clarifying their role in the information paradox.

Contribution

It introduces a high-analytic-control brane model to study extremal and non-extremal black holes and their quantum extremal islands without ensemble averaging assumptions.

Findings

Quantum extremal islands arise from RT surface phase transitions.

The model allows full Page curve calculations via two ODEs.

No quantum extremal islands found for extremal black holes in higher dimensions.

Abstract

We discuss holographic models of extremal and non-extremal black holes in contact with a bath in d dimensions, based on a brane world model introduced in arXiv:2006.04851. The main benefit of our setup is that it allows for a high degree of analytic control as compared to previous work in higher dimensions. We show that the appearance of quantum extremal islands in those models is a consequence of the well-understood phase transition of RT surfaces, and does not make any direct reference to ensemble averaging. For non-extremal black holes the appearance of quantum extremal islands has the right behaviour to avoid the information paradox in any dimension. We further show that for these models the calculation of the full Page curve is possible in any dimension. The calculation reduces to numerically solving two ODEs. In the case of extremal black holes in higher dimensions, we find no quantum extremal islands for a wide range of parameters. In two dimensions, our results agree with arXiv:1910.11077 at leading order; however a finite UV cutoff introduced by the brane results in subleading corrections. For example, these corrections result in the quantum extremal surfaces moving further outward from the horizon, and shifting the Page transition to a slightly earlier time.