On homogeneous 3-dimensional spacetimes: focus on plane waves

2022/10/20 by Souheib Allout, Allout, Souheib, Belkacem Abderrahmane +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · doi:10.48550/arxiv.2210.11439

openalex publication_date 2022/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the classification of Lorentz homogeneous spaces of dimension 3, and relax usual completeness assumptions. In particular, non-unimodular elliptic plane waves, and only them, are neither locally symmetric nor locally isometric to a left-invariant Lorentz metric on a 3-dimensional Lie group. We characterize homogeneous plane waves in dimension 3, and prove they are non-extendable, and geodesically complete only if they are symmetric. Finally, only one non-flat plane wave has a compact model.

Related

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