Islands in de Sitter space
Islands in de Sitter space
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DOI：
10.1007/jhep02(2021)072
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发表时间：
2020-08
影响因子：
5.4
通讯作者：
V. Balasubramanian;Arjun Kar;Tomonori Ugajin
中科院分区：
文献类型：
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作者：
V. Balasubramanian;Arjun Kar;Tomonori Ugajin
我们考虑耦合到CFT的2d de Sitter JT引力中的黑洞，并在不相交的非引力宇宙中与物质纠缠。追踪纠缠的物质会使CFT处于一个密度矩阵中，其应力张量对德西特几何产生反作用，从而延长了黑洞视界后面的虫洞。自然地，纠缠物质的熵随着纠缠强度的增加而无限制地增加，但一夫一妻制的性质预测这种增长必须保持平稳。我们计算的熵通过副本的技巧，包括虫洞之间的副本副本的德西特几何，并发现传统的场论纠缠熵和极端的德西特几何中的“岛屿”的表面积之间的竞争。黑洞和宇宙视界都在产生这种岛屿的反作用几何中发挥作用，并具有稳定一夫一妻制所需的熵增长的效果。我们首先展示了一个场景，其中德西特空间部分已被解压缩到一个区间。然后，我们考虑紧凑的几何，并主张在封闭宇宙的背景下，恢复佩奇曲线的岛屿公式的一个新的解释。最后，我们评论我们的建设应用于空de Sitter空间中的宇宙视界。
We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal “islands” in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the backreacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a scenario in which the de Sitter spatial section has been decompactified to an interval. Then we consider the compact geometry, and argue for a novel interpretation of the island formula in the context of closed universes that recovers the Page curve. Finally, we comment on the application of our construction to the cosmological horizon in empty de Sitter space.