标题： 哥德尔不完全性和黑洞信息悖论 显示英文标题

标题： Gödel Incompleteness and the Black Hole Information Paradox

摘要： 半经典推理表明，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，这个问题通常被称为黑洞信息悖论。此外，似乎无法唯一地预测有关坍缩物体的信息被局域化的具体位置。我们提出，这个悖论的后者可能反映了黑洞演化的半经典理论中不一致的自指问题。这暗示了半经典方法的不足，或者最坏的情况下，表明标准量子力学和广义相对论在根本上是不兼容的。对于局域化悖论的一种解决办法是识别出与一致性施加相关的哥德尔式的不完备性，并引入可能的新物理来填补这种不完备性。另一种解决办法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，包括永恒坍缩的物体、黑洞遗迹、黑洞最终态以及半经典量子引力的简单变体。 显示英文摘要

摘要： Semiclassical reasoning suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information, a problem often referred to as the black hole information paradox. Further, there seems to be no unique prediction of where the information about the collapsing body is localized. We propose that the latter aspect of the paradox may be a manifestation of an inconsistent self-reference in the semiclassical theory of black hole evolution. This suggests the inadequacy of the semiclassical approach or, at worst, that standard quantum mechanics and general relavity are fundamentally incompatible. One option for the resolution for the paradox in the localization 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.