Optimal version of the fundamental theorem of chronogeometry

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-09-11 DOI:10.1016/j.aim.2025.110528

Michiya Mori , Peter Šemrl

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引用次数: 0

Abstract

We study lightlikeness preserving mappings from the 4-dimensional Minkowski spacetime

M_{4}

to itself under no additional regularity assumptions like continuity, surjectivity, or injectivity. We prove that such a mapping ϕ satisfies one of the following three conditions.

(1)
The mapping ϕ can be written as a composition of a Lorentz transformation, a multiplication by a positive scalar, and a translation.
(2)
There is an event $r \in M_{4}$ such that $ϕ (M_{4} ∖ {r})$ is contained in one light cone.
(3)
There is a lightlike line ℓ such that $ϕ (M_{4} ∖ ℓ)$ is contained in another lightlike line.

Here, a line that is contained in some light cone in

M_{4}

is called a lightlike line. We also give several similar results on mappings defined on a certain subset of

M_{4}

or the compactification of

M_{4}

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时间几何基本定理的最佳版本

我们研究了从四维闵可夫斯基时空M4到自身的光相似性保持映射，没有额外的规则性假设，如连续性，满性或注入性。我们证明了这样的映射φ满足以下三个条件之一。(1)映射φ可以写成一个洛伦兹变换、一个正标量的乘法和一个平移的组合。(2)存在一个事件r∈M4，使得φ (M4∈{r})包含在一个光锥中。(3)存在一条类光线，使得φ (M4∈)包含在另一条类光线中。在这里，包含在M4中的某个光锥中的线被称为类光线。对于定义在M4的某个子集或M4的紧化上的映射，我们也给出了几个类似的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.