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<p>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.</p>

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On homogeneous 3-dimensional spacetimes: focus on plane waves

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月6日

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  • S. Allout,
  • A. Belkacem,
  • A. Zeghib

摘要

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.