Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island
Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island
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DOI：
10.1140/epjc/s10052-021-09680-x
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Wontae Kim;Mungon Nam
中科院分区：
文献类型：
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作者：
Wontae Kim;Mungon Nam
纠缠熵的岛规则被应用到一个永恒的Reissner-Nordström黑洞。关键的成分是，黑洞被假定为与任意温度的热浴处于热平衡，因此广义熵被视为离壳。将离壳广义熵与在壳条件相结合，求出离壳广义熵，然后根据孤岛规则得到纠缠熵。对于非极值黑洞，纠缠熵随时间线性增长，并在Page时间后达到饱和。纠缠熵也有一个明确的史瓦西极限。在极端黑洞中，岛式方案提供了随时间递增的纠缠熵，而在Page时间之后纠缠熵为常数。在极端黑洞中，岛的边界遇到曲率奇点，半经典近似出现无效。为了避免遇到曲率奇异性，我们将此方法应用于原点正则的海沃德黑洞。因此，极端黑洞中岛的存在可以提供有限的纠缠熵，这可能意味着极端黑洞的非平凡真空配置。
The island rule for the entanglement entropy is applied to an eternal Reissner–Nordström black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.