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Extremals of the induced sub-Lorentz structure on the Gödel universe
V. N. Berestovskii Sobolev Institute of Mathematics, Novosibirsk, Russia
Abstract:
We study the Gödel universe as the Lie group with the induced left-invariant sub-Lorentz structure defined by some proper subspace of the Lie algebra that generates it. We find the expressions for timelike and isotropic extremals in elementary functions by methods of geometric optimal control. Also, we prove that these extremals are not closed but as a rule not complete, having proper open subintervals of the real line as maximal connected domains.
Keywords:
Gödel universe, induced left-invariant sub-Lorentz structure, isotropic extremal, Lie algebra, Lie group, orthonormal basis, timelike extremal.
Received: 16.05.2024 Revised: 10.07.2024 Accepted: 20.08.2024
Citation:
V. N. Berestovskii, “Extremals of the induced sub-Lorentz structure on the Gödel universe”, Sibirsk. Mat. Zh., 65:6 (2024), 1115–1127; Siberian Math. J., 65:6 (2024), 1292–1304
Linking options:
https://www.mathnet.ru/eng/smj7913 https://www.mathnet.ru/eng/smj/v65/i6/p1115
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Abstract page: | 53 | Full-text PDF : | 1 | References: | 10 | First page: | 3 |
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