On smoothness of timelike maximal cylinders in three dimensional vacuum spacetimes

Mathematics – Differential Geometry

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Scientific paper

We show that timelike maximal cylinders in $\RR^{1 + 2}$ always develop
singularities in finite time and that, infinitesimally at a generic
singularity, their time slices are evolved by a rigid motion or a self-similar
motion. We also prove a mild generalization in non-flat backgrounds.

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