Entanglement Entropy of Black Holes.
Entanglement Entropy of Black Holes.
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黑洞的纠缠熵。
DOI：
10.12942/lrr-2011-8
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发表时间：
2011
影响因子：
40.6
通讯作者：
Solodukhin SN
中科院分区：
文献类型：
--
作者：
Solodukhin SN
纠缠熵是表征量子力学大系统中各子系统之间相互关系的基本量。对于被表面隔开的两个子系统，纠缠熵与表面的面积成正比，并取决于紫外截止，这调节了短程关联。当纠缠表面是黑洞视界时，纠缠熵计算的几何性质特别有趣。我回顾了各种方面的计算：有用的数学工具，如几何空间与圆锥奇点和热核方法，紫外发散的熵和重整化，对数项纠缠熵在四，六个维度和它们的关系的共形异常。在审查的重点是系统地使用圆锥奇点方法。与其他已知的方法，如't Hooft的砖墙模型和欧几里德路径积分的光学度规的关系进行了详细讨论。由于场的纠缠熵的令人困惑的行为，其中非最小耦合到引力，强调。黑洞视界纠缠熵的全息描述说明的二维和四维的例子。最后，我检查的可能性解释的贝肯斯坦-霍金熵完全纠缠熵。
The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.