Closed Timelike Curves in Flat Lorentz Spacetimes

Abstract

We consider the region of closed timelike curves (CTC&#39;s) in three-dimensional flat Lorentz spacetimes. The interest in this global geometrical feature goes beyond the purely mathematical. Such spacetimes may be considered lower-dimensional toy models of sourceless Einstein gravity or cosmology. In particular, our interest in this note will be to find the set free of CTC&#39;s for $E/<γ>$, where $E$ is modeled on Minkowski space and $γ$ is a Poincaré transformation. We describe the set free of CTC&#39;s where $γ$ is hyperbolic, parabolic and elliptic.