Journal Article

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole

Marolf, Donald, Engelhardt, Netta, Maxfield, Henry, Almheiri, Ahmed

2019

Overview

A bstract Bulk quantum fields are often said to contribute to the generalized entropy A 4 G N + S bulk only at O (1). Nonetheless, in the context of evaporating black holes, O (1 /GN ) gradients in S bulk can arise due to large boosts, introducing a quantum extremal surface far from any classical extremal surface. We examine the effect of such bulk quantum effects on quantum extremal surfaces (QESs) and the resulting entanglement wedge in a simple two-boundary 2 d bulk system defined by Jackiw-Teitelboim gravity coupled to a 1+1 CFT. Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side. We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scambling time β 2 π log ΔS + O 1 in accord with expectations for holographic implementations of the Hayden-Preskill protocol. We also find an interesting QES phase transition at what one might call the Page time for our process.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: 2D Gravity / AdS-CFT Correspondence / Black holes / Black Holes in String Theory / Classical and Quantum Gravitation / Elementary Particles / Entanglement / Entropy / Gauge- gravity correspondence / High energy physics / Phase transitions / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum Physics / Regular Article - Theoretical Physics / Relativity Theory / String Theory