标题： 广义相对论的奇点定理及其低正则性扩展 显示英文标题

标题： The singularity theorems of General Relativity and their low regularity extensions

摘要： 在罗杰·彭罗斯爵士2020年获得诺贝尔物理学奖之际，我们回顾广义相对论的奇点定理，以及它们最近对低正则性洛伦兹度量的扩展。 后者是出于探索经典定理所预测的奇点性质的追求。 针对更数学化的读者，我们提供了一个教学性的介绍，重点放在论证的分析方面。 我们特别集中在适当的几何和初始条件下，对因果测地线的聚焦结果，在光滑情况和低正则性情况下。 后者包括了通过正则化方法证明$C^1$-奇点定理的主要技术进展，该方法允许处理分布曲率。 最后，我们概述了相关研究方向和未来展望。 显示英文摘要

摘要： On the occasion of Sir Roger Penrose's 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent extension to Lorentzian metrics of low regularity. The latter is motivated by the quest to explore the nature of the singularities predicted by the classical theorems. Aiming at the more mathematically minded reader, we give a pedagogical introduction to the classical theorems with an emphasis on the analytical side of the arguments. We especially concentrate on focusing results for causal geodesics under appropriate geometric and initial conditions, in the smooth and in the low regularity case. The latter comprise the main technical advance that leads to the proofs of $C^1$-singularity theorems via a regularisation approach that allows to deal with the distributional curvature. We close with an overview on related lines of research and a future outlook.