Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended to gravitational systems. To gain insight into this question, we explore how this story is modified within the context of Karch-Randall braneworlds when we allow the asymptotic bath to couple to dynamical gravity. We find that because of the inability to separate degrees of freedom by spatial location when defining the radiation region, the entanglement entropy of radiation emitted into the bath is a time-independent constant, consistent with recent work on black hole information in asymptotically flat space. If we instead consider an entanglement entropy between two sectors of a specific division of the Hilbert space, we then find non-trivial time-dependence, with the Page time a monotonically decreasing function of the brane angle---provided both branes are below a particular angle. However, the properties of the entropy depend discontinuously on this angle, which is the first example of such discontinuous behavior for an AdS brane in AdS space.

中文翻译：

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带浴缸的信息传递

纠缠岛的后期优势在解决与渐近非重力浴耦合的AdS中黑洞的信息悖论中起着至关重要的作用。一个自然的问题是如何将这种观察扩展到重力系统。为了深入了解这个问题，我们探讨了当允许渐近浴耦合到动态引力时，如何在Karch-Randall braneworlds语境中修改此故事。我们发现，由于在定义辐射区域时无法通过空间位置分开自由度，因此发射到镀液中的辐射的纠缠熵是与时间无关的常数，这与最近关于渐近平坦空间中黑洞信息的研究一致。如果我们改为考虑希尔伯特空间的一个特定划分的两个扇区之间的纠缠熵，那么我们发现非平凡的时间依赖性，佩奇时间是米糠角的单调递减函数，前提是两个米糠都在一个特定角度。但是，熵的属性不连续地依赖于该角度，这是AdS空间中AdS麸皮这种不连续行为的第一个示例。