发表机构
Rutgers University（罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对AdS黑洞蒸发中的岛屿公式，论证岛屿量子信息集中于Page时间时靠近视界的微小类空区域，通过协变熵界和量子统计力学两种论据支持该结论。
AI 中文摘要
大型AdS黑洞的量子极值曲面岛屿公式，通过将AdS/CFT对应中的CFT耦合到外部系统使其蒸发，证明了如果黑洞内部的一个区域在Page时间之前与外部辐射纠缠，则时空图像可以重现CFT/浴系统量子力学所需的Page曲线。在“良好切片”坐标的有效量子场论（EFT）描述中，这似乎暗示了自Page时间之前很久就因果分离的自由度之间存在悖论性的纠缠。我们将给出两个论证，表明岛屿中的所有量子信息实际上都集中在Page时间时非常靠近黑洞视界的一个微小类空部分。第一个论证将协变熵界（CEB）应用于起源于将成为岛屿的类空区域（但在Page时间之前的某个时间切片上）的测地线的因果钻石。岛屿上除拉伸视界区域中非常靠近视界的点之外的所有点，其熵界仅为黑洞熵的极小部分。第二个论证使用标准量子统计力学结合CFT的张量网络重整化群正则化，论证微正则蒸发黑洞中典型纯态的波函数总是将其大部分概率集中在对应于对偶张量网络/AdS切片中一小段半径范围的窄波长范围内。
英文摘要
The Island Formula for Quantum Extremal Surfaces of large AdS black holes, which are made to evaporate by coupling the CFT of the AdS/CFT correspondence to an external system, demonstrates that the space time picture can reproduce the quantum mechanically required Page curve of the CFT/bath system if a region in the interior of the black hole has become entangled with the external radiation by the Page time. In an effective quantum field theory (EFT) description in ``nice slice" coordinates, this appears to imply paradoxical entanglement between degrees of freedom that have been causally disconnected since long before the Page time. We will give two arguments that all of the quantum information in the island is in fact concentrated in a tiny space-like portion of the island very close to the black hole horizon at the Page time. The first applies the covariant entropy bound\cite{fsb} (CEB) to the causal diamonds of geodesics originating on the space-like region that becomes the island, but on a time slice just before the Page time. All points on the island except those in a stretched horizon region very close to the horizon have entropy bounds that are tiny fractions of the black hole entropy. The second argument uses standard quantum statistical mechanics combined with the tensor network renormalization group regularization of CFT to argue that the wave function of a typical pure state in the microcanonical evaporating black hole always has most of its probability concentrated in a small range of wavelengths corresponding to a small range of radii in the dual tensor network/AdS slice.
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