The Gödel Universe as the Lie Group with left-invariant Lorentz metric

2024/04/10 by V. N. Berestovskiĭ, Berestovskii, V. N.
Earth and Planetary Sciences · Physics and Astronomy · #49J15 #53C30 #53C50 #83C20 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.2404.06866

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The author studies the Gödel Universe as the Lie group with left-invariant Lorentz metric. The expressions for timelike and isotropic geodesics in elementary functions are found by methods of geometric theory of optimal control for the search of geodesics on Lie groups with left-invariant (sub-)Lorentz metrics. It is proved that the Gödel Universe has no closed timelike or isotropic geodesics.

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