标题： 哥德尔不完全性与黑洞信息悖论 显示英文标题

标题： Gödel Incompleteness and the Black Hole Information Paradox

摘要： 黑洞信息悖论表明，一个物体坍缩成黑洞并通过发射霍金辐射蒸发的过程可能会破坏信息。 此外，似乎无法唯一预测关于坍缩物体的信息位于何处。 我们认为，悖论的这一方面是半经典黑洞演化理论中不一致的自指现象的表现。 这表明半经典方法的不足，或者标准量子力学与广义相对论在根本上不相容。 解决这一问题的一个选项是识别对应于一致性的类似哥德尔的不完备性，并引入可能的新物理来补充这种不完备性。 另一个选项是修改理论，以禁止自指。 我们讨论了实现这些选项的各种可能情景，包括永恒坍缩物体、黑洞残余物、黑洞最终状态以及半经典量子引力的简单变体。 显示英文摘要

摘要： The black hole information paradox suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information. Further, there seems to be no unique prediction on where the information about the collapsing body is localized. We argue that the latter aspect of the paradox is a manifestation of an inconsistent self-reference in the semiclassical theory of black hole evolution. This suggests the inadequacy of the semiclassical approach or that standard quantum mechanics and general relavity are fundamentally incompatible. One option for its resolution is to identify the G\"odel-like incompleteness that corresponds to an imposition of consistency, and introduce possibly new physics that supplies this incompleteness. Another option is to modify the theory in such a way as to prohibit self-reference. We discuss various possible scenarios to implement these options, including eternally collapsing objects, black hole remnants, black hole final states, and simple variants of semiclassical quantum gravity.