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

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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)

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

Received: 16.03.2024
Revised: 03.07.2024
Accepted: 20.08.2024

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

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}

\crossref{https://doi.org/10.33048/smzh.2024.65.503}

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Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	39
Full-text PDF :	3
References:	19
First page:	9

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