论文标题
一般相对论的奇异定理及其低规律性扩展
The singularity theorems of General Relativity and their low regularity extensions
论文作者
论文摘要
在罗杰·彭罗斯爵士（Roger Penrose）2020年诺贝尔物理学奖之际，我们回顾了一般相对性的奇异定理，以及他们最近扩展到洛伦兹（Lorentzian）的规律性低规律的指标。后者是出于探索经典定理预测的奇异性的性质而激发的。针对更具数学意义的读者，我们对经典定理进行教学介绍，重点是论证的分析方面。我们特别关注在适当的几何和初始条件下，在平滑的规律性情况下，在适当的几何条件和初始条件下为因果地球化学的聚焦结果。后者是通过正规化方法的$ c^1 $ singularity定理的证据的主要技术进步，该方法允许处理分配曲率。我们概述了相关研究线和未来前景。
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.
