Dirichlet Baths and the Not-so-Fine-Grained Page Curve

TL;DR

This paper introduces a Dirichlet-based holographic method for calculating entanglement entropy on gravitating branes, providing insights into the black hole information paradox and the role of gravity strength in holographic entanglement.

Contribution

It proposes a novel Dirichlet prescription for entanglement entropy in wedge holography, analyzing the interplay of gravity strength and extremal surfaces in resolving the information paradox.

Findings

The Dirichlet prescription yields consistent entanglement entropy results.

Weak gravity on the anchor is equivalent to no gravity in island physics.

An intricate interplay of extremal surfaces influences the presence of islands.

Abstract

We present a doubly holographic prescription for computing entanglement entropy on a gravitating brane. It involves a Ryu-Takayanagi surface with a Dirichlet anchoring condition. In braneworld cosmology, a related approach was used previously in arXiv:2007.06551. There, the prescription naturally computed a co-moving entanglement entropy, and was argued to resolve the information paradox for a black hole living in the cosmology. In this paper, we show that the Dirichlet prescription leads to reasonable results, when applied to a recently studied wedge holography set up with a gravitating bath. The nature of the information paradox and its resolution in our Dirichlet problem have a natural understanding in terms of the strength of gravity on the two branes and at the anchoring location. By sliding the anchor to the defect, we demonstrate that the limit where gravity decouples from the anchor is continuous -- in other words, as far as island physics is considered, weak gravity on the anchor is identical to no gravity. The weak and (moderately) strong gravity regions on the brane are separated by a "Dirichlet wall". We find an intricate interplay between various extremal surfaces, with an island coming to the rescue whenever there is an information paradox. This is despite the presence of massless gravitons in the spectrum. The overall physics is consistent with the slogan that gravity becomes "more holographic", as it gets stronger. Our observations strengthen the case that the conventional Page curve is indeed of significance, when discussing the information paradox in flat space. We work in high enough dimensions so that the graviton is non-trivial, and our results are in line with the previous discussions on gravitating baths in arXiv:2005.02993 and arXiv:2007.06551.