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

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.

The Dictionary for Double Holography and Graviton Masses in d Dimensions

“…In the second part of the paper we used this dictionary to derive a formula for the mass of the graviton in the brane theory. The question whether graviton masses are important for the island formula has been discussed in [5,53,54]. One interesting observation to make is that apart from the near boundary limit, the formula for the graviton mass exhibits The solid line is computed numerically.…”

AdS/BCFT and Island for curvature-squared gravity

“…Recently, a great breakthrough towards the resolution of the black hole information paradox has been made [1,2], where double holography and island play an important role. See [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] for some recent works. As a generalization of the AdS/CFT correspondence [31,32,33], double holography has a close relation to brane world theory [34,35,36] and AdS/BCFT [37,38,39,40,41,42,43].…”

Entropy of Hawking Radiation for Two-Sided Hyperscaling Violating Black Branes

“…Second, replica wormhole saddle which is a wormhole connecting various copies of the original black hole. It was observed that the replica saddle leads to the contribution of the islands and enforces the entropy Furthermore, the island rule have been explored extensively for various black holes in flat and AdS spacetimes such as: JT gravity [9,[17][18][19][25][26][27][28], two-dimensional dilaton gravity [29][30][31][32][33] , in higher dimensions [33][34][35][36][37][38][39][40][41][42], higher derivative gravity theories [43], charged black holes [44][45][46][47], pure BTZ black hole microstates 3 [48][49][50], and black holes coupled to gravitating baths [50][51][52][53]. See also [4] for a very nice review on the topic.…”