Massive islands
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Springer
Received: July 15, 2020 Accepted: August 17, 2020 Published: September 17, 2020
Hao Geng and Andreas Karch Department of Physics, University of Washington, Seattle, WA, 98195-1560, U.S.A.
E-mail: [email protected], [email protected] Abstract: We comment on the role of the graviton mass in recent calculations of the Page curve using holographic ideas. All reliable calculations of the Page curve in more than 2+1 spacetime dimensions have been performed in systems with massive gravitons. A crucial ingredient in these calculations is the formation of islands, regions that contribute to the entropy of degrees of freedom located elsewhere. While most often simply ignored, it is indeed true that mass of the graviton does not appear to significantly affect the calculations that appeared in the literature. We use the freedom to change the graviton mass to give an extremely simple model of analytically tractable island formation in general dimensions. We do however note that if one attempts to take the limit of zero graviton mass, any contribution from the islands disappears. This raises the question to what extent entanglement islands can play a role in standard massless gravity. Keywords: AdS-CFT Correspondence, Black Holes, Black Holes in String Theory, Conformal Field Models in String Theory ArXiv ePrint: 2006.02438
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)121
JHEP09(2020)121
Massive islands
Contents 1 Introduction
1
2 Massive RS gravity
5
3 Islands and black holes
8
5 Massless gravitons
1
15
Introduction
One of the most exciting developments in the last year in our understanding of quantum gravity has been the demonstration that the Page curve [1], the conjectured time evolution of the entanglement between an evaporating black hole and its Hawking radiation, in certain simplified models of quantum gravity can be rigorously calculated using ideas from holography. For a recent easy to read review of these developments see [2]. In order to have a theory of quantum gravity that is under theoretical control one wants to study black holes in (asymptotically) anti-de Sitter (AdS) space so one has a non-perturbative definition of quantum gravity in terms of the AdS/CFT correspondence. Since AdS effectively acts as a box, large black holes in AdS do not evaporate. In order to get a tractable model of an evaporating black hole in AdS, the authors of [3, 4] impose transparent boundary conditions on AdS, allowing radiation reaching the boundary of AdS to couple to an external heat bath. AdS with transparent boundary conditions has been explored extensively long before holographic calculations of the Page curves required to revisit this system. In [5, 6] it was argued, that a d dimensional holographic field theory on a space with boundaries has three equivalent descriptions: 1. as a d dimensional conformal field theory with a d−1 dimensional boundary (BCFTd ) 2. as gravity in an AdSd+1 with an AdSd Randall-Sundrum (RS) [7] brane 3. as a d dimensional CFT living on
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