We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for “islands” in determining the entanglement wedge.

中文翻译：

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半经典几何霍金辐射的佩奇曲线

我们考虑与物质耦合的引力理论，其中物质具有更高维的全息对偶。在这样的理论中，寻找量子极值面就等同于寻找高维理论中的 RT/HRT 面。我们使用它计算霍金辐射的熵，并认为它遵循佩奇曲线，正如最近对旧黑洞的熵和纠缠楔的计算所暗示的那样。更高维的几何结构本着 ER=EPR 的精神将辐射连接到黑洞内部。黑洞内部随后成为辐射纠缠楔的一部分。受此启发，我们提出了计算与引力系统纠缠的量子系统熵的新规则，该规则涉及在确定纠缠楔时寻找“孤岛”。