标题： 时间几何学基本定理的最优版本 显示英文标题

标题： Optimal version of the fundamental theorem of chronogeometry

摘要： 我们研究从$4$维闵可夫斯基时空$\mathcal{M}_4$到自身的保持类光性的映射，在没有额外的正则性假设如连续性、满射性或单射性的情况下。 我们证明这样的映射$\phi$满足以下三个条件中的一个。 (1) 映射$\phi$可以写成洛伦兹变换、正标量乘法和平移的复合。 (2) 存在一个事件$r\in \mathcal{M}_4$，使得$\phi(\mathcal{M}_4\setminus\{r\})$包含在一个光锥中。 (3) 存在一条类光直线$\ell$，使得$\phi(\mathcal{M}_4\setminus \ell)$包含在另一条类光直线中。 这里，包含在$\mathcal{M}_4$中某个光锥内的直线称为类光直线。 我们还给出了关于定义在$\mathcal{M}_4$的某个子集或$\mathcal{M}_4$的紧化空间上的映射的几个类似结果。 显示英文摘要

摘要： We study lightlikeness preserving mappings from the $4$-dimensional Minkowski spacetime $\mathcal{M}_4$ to itself under no additional regularity assumptions like continuity, surjectivity, or injectivity. We prove that such a mapping $\phi$ satisfies one of the following three conditions. (1) The mapping $\phi$ can be written as a composition of a Lorentz transformation, a multiplication by a positive scalar, and a translation. (2) There is an event $r\in \mathcal{M}_4$ such that $\phi(\mathcal{M}_4\setminus\{r\})$ is contained in one light cone. (3) There is a lightlike line $\ell$ such that $\phi(\mathcal{M}_4\setminus \ell)$ is contained in another lightlike line. Here, a line that is contained in some light cone in $\mathcal{M}_4$ is called a lightlike line. We also give several similar results on mappings defined on a certain subset of $\mathcal{M}_4$ or the compactification of $\mathcal{M}_4$.