Double Holography as a Model for Black Hole Complementarity
Double Holography as a Model for Black Hole Complementarity
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发表时间：
2021
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通讯作者：
Dominik Neuenfeld
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作者：
Dominik Neuenfeld
本文研究了黑洞与浴槽耦合的双全息模型中不同熵测度之间的关系。该模型将一个d+ 1维的AdS体与两个d维的公式——膜和边界透视——联系起来。本文认为，Ryu-Takayanagi曲面的同调约束，其面积计算冯·诺伊曼熵，取决于采取哪一个d维视角。其结果是，边界透视图中的冯·诺伊曼熵等于膜透视图中的细粒度熵，这是使用孤岛处方计算的。类似地，膜描述中的冯·诺伊曼熵等于边界透视中的粗粒度熵。作用于辐射的简单算符在两种表述中是相同的，而复算符则是非局部映射。本文介绍了一个简单的玩具模型，以说明两种系统描述之间的这种映射是如何产生岛屿公式和虫洞的。最后，我们推测黑洞互补的实现类似于双全息的情况。黑洞既可以被描述为结构接近视界的量子引力物体，也可以被描述为遵循等效原理但从不释放信息的半经典黑洞。后一种描述只有在我们允许观察者只使用足够简单的操作符时才有效。在任何一种描述中，信息都不会被克隆。
This paper studies the relation between different measures of entropy in a doubly-holographic model of a black hole coupled to a bath. The model relates a d+ 1-dimensional AdS bulk to two d-dimensional formulations – the brane and the boundary perspective. It is argued that the homology constraint for Ryu-Takayanagi surfaces, whose area computes von Neumann entropy, depends on which of the d-dimensional perspectives is taken. As a consequence it follows that the von Neumann entropy in the boundary perspective equals the fine-grained entropy in the brane perspective, which is computed using the island prescription. Similarly, the von Neumann entropy in the brane description equals a coarse grained entropy in the boundary perspective. Simple operators which act on the radiation are identical in both formulations, while complex operators map non-locally. A simple toy model is introduced to demonstrate how such a map between two descriptions of the system gives rise to the island formula and wormholes. Lastly, it is conjectured that black hole complementarity is realized analogously to the doubly-holographic situation. A black hole can either be described as quantum gravitational object with structure near the horizon, or as a semi-classical black hole which respects the equivalence principle but never releases its information. The latter description is only valid if we allow observers to only act with sufficiently simple operators. Information is never cloned in either description.