发表机构
Dipartimento di Matematica, Università degli Studi di Pisa; Department of Mathematics, University of Toronto; Department of Mathematics, University of Osaka; RIKEN Center for Advanced Intelligence Project (AIP); Department of Mathematics, University of Vienna（比萨大学数学系; 多伦多大学数学系; 大阪大学数学系; 理化学研究所先进智能研究中心; 维也纳大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对混合水平/垂直正则性的洛伦兹-芬斯勒结构，通过两阶段近似程序证明了霍金与彭罗斯奇性定理，将Graf的C¹奇性定理推广至C¹加权情形。
AI 中文摘要
我们针对混合水平/垂直正则性的洛伦兹-芬斯勒结构证明了霍金与彭罗斯奇性定理：在C¹加权情形下正则性为C⁽¹,²⁾，在非加权情形下为C⁽¹,³⁾。在此正则性下，测地线未必由初始条件唯一确定，且（加权）里奇曲率需按分布意义诠释。我们的方法依赖于两阶段近似程序：一是保齐性卷积，该方法在更广的半黎曼-芬斯勒框架中具有独立价值；二是Chruściel-Grant型适配因果性的近似。在C¹洛伦兹度量的特殊情形中，我们的结果将Graf的C¹奇性定理推广至C¹加权情形。
英文摘要
We prove the Hawking and Penrose singularity theorems for Lorentz--Finsler structures of mixed horizontal/vertical regularity $C^{(1,2)}$ in the $C^1$ weighted case and $C^{(1,3)}$ in the unweighted case. At this regularity, geodesics need not be uniquely determined by their initial conditions, and the (weighted) Ricci curvature must be interpreted distributionally. Our approach relies on a two-stage approximation procedure: first, a homogeneity-preserving convolution, which is of independent interest in the broader semi-Riemann--Finsler setting, and second, a causality-adapted approximation à la Chruściel--Grant. In the special case of $C^1$ Lorentzian metrics, our results extend the $C^1$ singularity theorems of Graf to the $C^1$ weighted case.
Comments48 pages, comments welcome
