Timelike and Isotropic Geodesics of the Gödel Universe as a Lie Group with Left-Invariant Lorentz Metric.

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. [ABSTRACT FROM AUTHOR]