标题： 超普朗克尺度的因果性与时空奇点 显示英文标题

标题： Trans-Planckian censorship and spacetime singularities

摘要： 我们研究了跨普朗克宇宙禁令猜想（TCC）边界对时空测地线完备性的影响以及无限固有时存在的相关性。 使用格龙沃尔引理，可以直接推导出TCC边界，从而得出不存在爆破解的结果。 我们表明，TCC提供了测地线完备性所需标准的一部分，然后我们提供了其余的标准——外曲率范数远离零的有界性。 我们还讨论了这些结果在全局和正则双曲性假设下对于弗里德曼宇宙经典演化的意义。 显示英文摘要

摘要： We study the effects of trans-planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall's lemma, TCC bounds can be derived directly, leading to a result about the absence of blowup solutions. We show that the TCC provides part of the required criteria for geodesic completeness, and we then provide the remaining ones - the norm of the extrinsic curvature being bounded away from zero. We also discuss the importance of these results for the classical evolution of Friedmann universes under the assumptions of global and regular hyperbolicity.