On smoothness of timelike maximal cylinders in three-dimensional vacuum spacetimes

Abstract

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