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arXiv · 2210.11439

On homogeneous 3-dimensional spacetimes: focus on plane waves

Souheib Allout·Abderrahmane Belkacem·Abdelghani Zeghib
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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.

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Souheib Allout, Abderrahmane Belkacem, Abdelghani Zeghib. 2022-10-20. On homogeneous 3-dimensional spacetimes: focus on plane waves. https://arxiv.org/abs/2210.11439

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