Hawking’s discovery that black holes can evaporate through radiation emission has posed a number of questions that with time became fundamental hallmarks for a quantum theory of gravity. The most famous one is likely the information paradox, which finds an elegant explanation in the Page argument suggesting that a black hole and its radiation can be effectively represented by a random state of qubits. Leveraging the same assumption, we ponder the extent to which a black hole may display emergent symmetries, employing the entanglement asymmetry as a modern, information-based indicator of symmetry breaking. We find that for a random state devoid of any symmetry, a $U(1)$ symmetry emerges and it is exact in the thermodynamic limit before the Page time. At the Page time, the entanglement asymmetry shows a finite jump to a large value. Our findings imply that the emitted radiation is symmetric up to the Page time and then undergoes a sharp transition. Conversely the black hole is symmetric only after the Page time.

中文翻译：

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黑洞辐射的纠缠不对称性研究


霍金发现黑洞可以通过辐射发射而蒸发，这提出了许多问题，随着时间的推移，这些问题成为量子引力论的基本标志。最著名的一个可能是信息悖论，它在佩奇论证中找到了一个优雅的解释，表明黑洞及其辐射可以用量子位的随机状态有效地表示。利用相同的假设，我们思考黑洞可能显示出涌现对称性的程度，利用纠缠不对称性作为现代的、基于信息的对称性破缺指标。我们发现对于没有任何对称性的随机状态， $U(1)$ 对称性出现，并且在页面时间之前的热力学极限中是精确的。在页面时间，纠缠不对称性显示出有限跳跃到一个大值。我们的研究结果表明，发射的辐射在页面时间之前是对称的，然后经历急剧的转变。相反，黑洞只有在页面时间之后才是对称的。