We study the Page curve and the island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection with the ER=EPR proposal. We consider several models of two entangled 2d black holes in Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first, "doubled PSSY," model is one in which the black holes have end-of-the-world (ETW) branes with a flavour degree of freedom. We study highly entangled states of this flavour degree of freedom and find an entanglement-induced Hawking-Page-like transition from a geometry with two disconnected black holes to one with a pair of black holes connected by a wormhole, thus realising the ER = EPR proposal. The second model is a dynamical one in which the ETW branes do not have internal degrees of freedom but the JT gravity is coupled to a 2d CFT, and we entangle the black holes by coupling the two CFTs at the $AdS$ boundary and evolving for a long time. We study the entanglement entropy between the two black holes and find that the story is substantially similar to that with a non-gravitating thermal bath. In the third model, we couple the two ends of a two-sided eternal black hole and evolve for a long time. Finally, we discuss the possibility of a Hawking-Page-like transition induced by real-time evolution that realises the ER = EPR proposal in this dynamical setting.
考虑耦合到CFT的2d de Sitter JT引力场中的黑洞，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，其应力张量反作用于德西特几何，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“岛屿”的德西特几何的表面积之间的竞争。黑洞和宇宙视界都在反作用几何中产生这样的岛中起作用，并且具有稳定一夫一妻制所要求的熵增长的作用。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。
Black Hole Interior and Quantum Error Correction with Dynamical Gravity
Center for Gravitational Physics and Quantum Information (CGPQI), Yukawa Institute for Theoretical Physics (YITP), Kyoto University（京都大学引力物理与量子信息中心（CGPQI），理论物理汤川研究所（YITP））；Department of Physics, Rikkyo University（立教大学物理系）
