arXiv 2109.016392021-09hep-thgr-qcquant-ph

信息存储与近视界量子关联

Information storage and near horizon quantum correlations

Abram Akal

备注：: 8 pages, 5 figures; v2: 9 pages, metadata update, minor text edits, more clarifications, references added; v3: 10 pages, more improvements and clarifications (particularly in sec. IV), refs added

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AI总结：

本文研究量子黑洞的信息存储区域，指出在黑洞与 Hawking 辐射最大关联时熵球必须扩大，并将其归因于穿越黑洞大气层的不可见量子关联及量子引力幺正化效应。

摘要：

通常认为，与 Bekenstein-Hawking 熵相关的信息存储区域被一个直径等于两倍 Schwarzschild 半径的球所包围。我们指出，这不适用于量子黑洞。当量子黑洞与其 Hawking 辐射达到最大关联时，这一偏差会尤为明显。具体而言，我们证明，当细粒度辐射熵达到最大值时，与底层微观结构相关的熵球尺寸必须扩大。这种扩大被理解为量子引力中幺正化效应的结果，并与全息原理近期的研究结果一致，后者认为纯化是通过延伸穿过黑洞大气层、在半经典层面不可见的量子关联实现的。在本工作中，我们考虑渐近平直时空中的一个蒸发黑洞。我们假设，只要从外部观察黑洞仍足够大，标准热力学描述就是有效的；逸入未来零无穷远的辐射可以在光滑时空背景上描述，并且 Hawking 辐射的 von Neumann 熵幺正演化。我们还简要评论了黑洞奇点。

英文摘要：

It is usually stated that the information storing region associated with the Bekenstein-Hawking entropy is enclosed by a sphere of diameter equal twice the Schwarzschild radius. We point out that this cannot apply to a quantum black hole. The deviation is particularly revealed when the latter is maximally correlated with its Hawking radiation. Specifically, we demonstrate that the size of the entropy sphere associated with the underlying microstructure has to be necessarily broadened when the fine grained radiation entropy becomes maximal. Such an enlargement is understood to be the consequence of unitarization effects in quantum gravity and aligns with recent findings in holography arguing that purification happens via semiclassically invisible quantum correlations extending across the black hole atmosphere. In the present work, we consider an evaporating black hole in asymptotically flat spacetime. We assume that the standard thermodynamical description is valid so long the black hole viewed from the outside is sufficiently large, radiation escaping into the future null infinity can be described on a smooth spacetime background, and the von Neumann entropy of Hawking radiation evolves unitarily. We briefly comment on the black hole singularity.

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