| Title: | Optimal version of the fundamental theorem of chronogeometry |
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| Authors: | ID Mori, Michiya (Author)
ID Šemrl, Peter (Author) |
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| Files: |  PDF - Presentation file, download (2,86 MB)
MD5: 97AAFB0EC9379F2A5ACFFC55B1525C6B
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0001870825004268
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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 $\mathcal{M}_4$. |
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| Keywords: | fundamental theorem of chronogeometry, special relativity, coherency preserving mapping |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.11.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 85 str. |
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| Numbering: | Vol. 480, part C, article no. 110528 |
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| PID: | 20.500.12556/DiRROS-23879  |
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| UDC: | 530.12:514.7 |
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| ISSN on article: | 0001-8708 |
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| DOI: | 10.1016/j.aim.2025.110528 |
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| COBISS.SI-ID: | 253408515 |
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| Note: |
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| Publication date in DiRROS: | 16.10.2025 |
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| Views: | 200 |
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| Downloads: | 87 |
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| Metadata: |    |
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