标题： 纠缠岛屿和单侧带电黑洞的Page曲线 显示英文标题

标题： Entanglement island and Page curve for one-sided charged black hole

摘要： 在本文中，我们扩展了使用“in”真空态计算黑洞霍金辐射纠缠熵的方法，该方法描述由引力坍缩形成的单侧渐近平坦中性黑洞，以适用于动态带电黑洞。 我们探讨了电荷对岛屿边界$\partial I$位置和Page时间的影响。 由于它们不同的几何结构，我们分别讨论了非极端和极端带电黑洞。 在非极端情况下，岛屿的出现使熵的界限在晚期得到保存，霍金辐射的纠缠熵满足Page曲线。 此外，我们还发现岛屿边界$\partial I$的位置取决于截断表面（观察者）的位置，这与永恒带电黑洞中的行为不同。 在极端黑洞中，当存在岛屿时，纠缠熵大约等于贝肯斯坦-霍金熵，而当没有岛屿时，纠缠熵变得无定义。 我们的分析强调了不同的几何配置如何显著影响熵的行为。 显示英文摘要

摘要： In this paper, we extend the method of calculating the entanglement entropy of Hawking radiation of black holes using the "in" vacuum state, which describes one-sided asymptotically flat neutral black hole formed by gravitational collapse, to dynamic charged black holes. We explore the influence of charge on the position of the boundary of island $\partial I$ and the Page time. Due to their distinct geometric structures, we discuss non-extremal and extremal charged black holes separately. In non-extremal cases, the emergence of island saves the bound of entropy at late times, and the entanglement entropy of Hawking radiation satisfies the Page curve. Moreover, we also find that the position of the boundary of island $\partial I$ depends on the position of the cutoff surface (observers), differing from the behavior in eternal charged black holes. In extremal black holes, when the island exists, the entanglement entropy is approximately equal to the Bekenstein-Hawking entropy, while the entanglement entropy becomes ill-defined when island is absent. Our analysis underscores how different geometric configurations significantly influence the behavior of entropy.