The large- N limit of asymptotically flat two-dimensional dilaton gravity coupled to N free matter fields provides a useful toy model for semiclassical black holes and the information paradox. Analyses of the asymptotic information flux as given by the entanglement entropy show that it follows the Hawking curve, indicating that information is destroyed in these models. Recently, motivated by developments in AdS/CFT, a semiclassical island rule for entropy has been proposed. We define and compute the island rule entropy for black hole formation and evaporation in the large- N RST model of dilaton gravity and show that, in contrast, it follows the unitary Page curve. The relation of these two observations, and interesting properties of the dilaton gravity island rule, are discussed.

中文翻译：

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渐近平坦的二维重力中的岛屿

与 N 自由物质场耦合的渐近平坦二维膨胀子引力的大 N 极限为半经典黑洞和信息悖论提供了一个有用的玩具模型。对纠缠熵给出的渐近信息通量的分析表明它遵循霍金曲线，表明这些模型中的信息被破坏了。最近，受 AdS/CFT 发展的推动，提出了一种半经典的熵岛规则。我们定义并计算了膨胀子引力的大 N RST 模型中黑洞形成和蒸发的岛规则熵，并表明，相比之下，它遵循幺正 Page 曲线。讨论了这两个观察结果的关系，以及膨胀子重力岛规则的有趣特性。