On homogeneous 3-dimensional spacetimes: focus on plane waves
Résumé
We revisit the classification of Lorentz homogeneous spaces of dimension 3, fixing statements in the literature and relaxing usual completeness assumptions. In particular, 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, 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.