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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 5, Pages 795–807
DOI: https://doi.org/10.33048/smzh.2024.65.503 (Mi smj7892) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Timelike and isotropic geodesics of the Gödel universe as a Lie group with left-invariant Lorentz metric

V. N. Berestovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2024.65.503
Abstract: Studying the Gödel universe as a Lie group with left-invariant Lorentz metric and using the methods of geometric theory of the optimal control for the search of geodesics on Lie groups with left-invariant (sub-)Lorentz metrics, we find the expressions for timelike and isotropic geodesics in elementary functions. Also, we pay special attention to proving that the Gödel universe has no closed timelike or isotropic geodesics.
Keywords: closed isotropic curve, closed timelike curve, Gödel universe, left-invariant Lorentz metric, Lie group, isotropic geodesic, timelike geodesic.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0006
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).
Received: 16.03.2024
Revised: 03.07.2024
Accepted: 20.08.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 5, Pages 1003–1014
DOI: https://doi.org/10.1134/S0037446624050033
Document Type: Article
UDC: 514.82+512.81+517.977
MSC: 35R30
Language: Russian
Citation: V. N. Berestovskii, “Timelike and isotropic geodesics of the Gödel universe as a Lie group with left-invariant Lorentz metric”, Sibirsk. Mat. Zh., 65:5 (2024), 795–807; Siberian Math. J., 65:5 (2024), 1003–1014
Citation in format AMSBIB
\Bibitem{Ber24}
\by V.~N.~Berestovskii
\paper Timelike and isotropic geodesics of the G\"odel universe as a~Lie group with left-invariant Lorentz metric
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 5
\pages 795--807
\mathnet{http://mi.mathnet.ru/smj7892}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 5
\pages 1003--1014
\crossref{https://doi.org/10.1134/S0037446624050033}
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