Information Transfer with a Gravitating Bath

TL;DR

This paper investigates how entanglement entropy and information transfer in black holes are affected when extending island concepts to gravitational systems within Karch-Randall braneworlds, revealing novel discontinuous behaviors.

Contribution

It extends the entanglement island framework to dynamical gravity in braneworlds, uncovering discontinuous entropy properties and the dependence of Page time on brane angles.

Findings

Entanglement entropy into the bath is time-independent and constant.

Non-trivial time dependence appears when considering Hilbert space divisions.

Page time decreases monotonically with brane angle, with discontinuous properties.

Abstract

Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended to gravitational systems. To gain insight into this question, we explore how this story is modified within the context of Karch-Randall braneworlds when we allow the asymptotic bath to couple to dynamical gravity. We find that because of the inability to separate degrees of freedom by spatial location when defining the radiation region, the entanglement entropy of radiation emitted into the bath is a time-independent constant, consistent with recent work on black hole information in asymptotically flat space. If we instead consider an entanglement entropy between two sectors of a specific division of the Hilbert space, we then find non-trivial time-dependence, with the Page time a monotonically decreasing function of the brane angle -- provided both branes are below a particular angle. However, the properties of the entropy depend discontinuously on this angle, which is the first example of such discontinuous behavior for an AdS brane in AdS space.