Abstract
We discuss a doubly-holographic prescription for black holes in braneworlds with a vanishing cosmological constant. It involves calculating Ryu-Takayanagi surfaces in AdS black funnel spacetimes attached to braneworld black holes in the critical Randall- Sundrum II model. Critical braneworlds have the virtue of having massless gravitons. Our approach should be useful when the braneworld is a cosmological black hole interacting with deconfined, large-N matter. In higher dimensions, explicit funnel metrics will have to be constructed numerically — but based on the general structure of the geometry, we present a natural guess for where one might find the semi-classical island. In a 3-dimensional example where a toy analytic black funnel is known, we can check our guess by direct calculation. We argue that this resolves a version of the information paradox in these braneworld systems, by finding strong evidence for “cosmological islands”. Comoving Ryu-Takayanagi surfaces and associated UV cut-offs on the brane, play natural roles.
Highlights
Take this to mean that the entanglement wedge/QES arguments of [5, 6] are the natural way to think of islands when the brane matter is a weakly coupled non-holographic theory, while the doubly holographic formulation of [8, 9] is the natural language when the brane matter is a deconfined large-N theory
The spatial boundary of flat space does not lend itself to a direct adaptation of the notion of a subregion, but it turned out that despite this, Asymptotic Causal Diamonds (ACD)-inspired ideas lead to natural definitions of QES and bulk entanglement wedges
We will argue that black funnels [28] anchored to braneworld black holes lead to a natural geometrization, and that holographic entanglement entropy computed in black funnel geometries give evidence for the existence of islands
Summary
The simplest context where we can hope to argue for the existence of semi-classical islands is when the braneworld gravity is coupled to holographic (i.e., strongly coupled, large central charge) matter that is deconfined. Even though analytic solutions are not known, there do exist numerical black funnel solutions in AdS5 [30] that are dual to asymptotically flat boundary Schwarzschild black holes. We will take this as conclusive evidence that black funnels are the holographic description of strongly coupled Hartle-Hawking states on the boundary of AdS. In a very interesting paper [39] (see [40]), Figueras and Wiseman have shown that braneworld black holes can be constructed from the associated AdSCFT problem They argued that given an asymptotic boundary metric and the demand that the behavior of the solution matches with AdS at the Poincare horizon, one can construct corresponding braneworld geometries that are solutions of the induced braneworld gravity. We will be able to do some concrete checks of our prescription using the toy analytic black funnel constructed in AdS3 by [28]
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