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.
Highlights
JHEP08(2021)119 this paper we will present a calculation that provides evidence that this worry is misplaced in the context of some of the recent questions regarding the information paradox
We show that the Dirichlet prescription leads to reasonable results, when applied to a recently studied wedge holography set up with a gravitating bath
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
Summary
We consider a doubly holographic set up where two subcritical KR branes are embedded into an AdS black string wedge, see [13] for details. We will be interested in finding Mathur-Hartman-Maldacena (MHM) surfaces We parametrize these surface as μ(u) and impose Neumann boundary conditions at the horizon. We will be interested in Dirichlet anchoring the RT surfaces at arbitrary locations on the branes This means that we will have to solve the above equations of motion numerically. The blue (island) curves that land on the physical brane with a Neumann boundary condition are finite, and resolve the information paradox at late times, with a non-trivial Page curve. For this class of curves, the structure of island physics near the defect is isomorphic to that at the defect found in [13]. We show the near-horizon region of these curves in a zoomed-in figure 2 to emphasize that everything is as it should be, and the boundary condition at the horizon is Neumann
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