Optimal version of the fundamental theorem of chronogeometry

Mori, Michiya (avtor), Šemrl, Peter (avtor)

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 $\mathcal{M}_4$.

• Jezik: Angleški jezik
• Ključne besede: fundamental theorem of chronogeometry, special relativity, coherency preserving mapping
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.11.2025
• Leto izida: 2025
• Št. strani: 85 str.
• Številčenje: Vol. 480, part C, art. no. 110528
• PID: 20.500.12556/RUL-175109
• UDK: 530.12:514.7
• ISSN pri članku: 0001-8708
• DOI: 10.1016/j.aim.2025.110528
• COBISS.SI-ID: 253408515
• Datum objave v RUL: 16.10.2025

Gradivo je del revije

• Naslov: Advances in mathematics
• Skrajšan naslov: Adv. math.
• Založnik: Elsevier
• ISSN: 0001-8708
• COBISS.SI-ID: 24891904

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.