基于热力学第一定律的黑洞纠缠熵

中文摘要 AI 辅助

我们通过沿由霍金温度标记的一参数平衡背景族积分热力学第一定律，完全在壳上计算具有基林视界的时空中量子物质的纠缠熵。这得到了一个用重整化应力-能量张量和基林矢量表示的闭式表达式，该表达式在构造上是有限的，无需复制和锥形奇点。其协变形式与巴丁-卡特-霍金质量变分公式的物质项一致。我们详细证明，对于德西特空间的静态片和非旋转BTZ黑洞，它能精确再现包含接触项Q的锥形熵。

英文摘要

We compute the entanglement entropy of quantum matter in spacetimes with a Killing horizon entirely on-shell, by integrating the first law of thermodynamics along a one-parameter family of equilibrium backgrounds labelled by the Hawking temperature. This yields a closed expression in terms of the renormalized stress-energy tensor and the Killing vector, finite by construction, with no replicas and no conical singularities. Its covariant form agrees with the matter terms of the Bardeen--Carter--Hawking mass variation formula. We show in details that for static patch of de Sitter space and for the non-rotating BTZ black hole it reproduces the conical entropy exactly, contact term $Q$ included.

发表机构

• Moscow Institute of Physics and Technology（莫斯科物理技术学院）
• Institute for Information Transmission Problems（信息传输问题研究所）

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