English

The G\"odel Universe as the Lie Group with left-invariant Lorentz metric

Differential Geometry 2024-04-11 v1

Abstract

The author studies the G\"odel 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 G\"odel Universe has no closed timelike or isotropic geodesics.

Keywords

Cite

@article{arxiv.2404.06866,
  title  = {The G\"odel Universe as the Lie Group with left-invariant Lorentz metric},
  author = {V. N. Berestovskii},
  journal= {arXiv preprint arXiv:2404.06866},
  year   = {2024}
}

Comments

16 p