(2+1)-DIMENSIONAL SPACETIMES CONTAINING CLOSED TIME-LIKE CURVES

We investigate the global geometries of (2+1)-dimensional spacetimes as characterized by the transformations undergone by tangent spaces upon parallel transport around closed curves. We critically discuss the use of the term total energy-momentum as a label for such parallel-transport transformations, pointing out several problems with it. We then investigate parallel-transport transformations in the known (2+1)-dimensional spacetimes containing closed timelike curves (CTCs), and introduce a few new such spacetimes. Using the more specific concept of the holonomy of a closed curve, applicable in simply connected spacetimes, we emphasize that Gotts two-particle CTC-containing spacetime does not have a tachyonic geometry. Finally, we prove the following modified version of Kabats conjecture: if a CTC is deformable to spacelike or null infinity while remaining a CTC, then its parallel-transport transformation cannot be a rotation; therefore its holonomy, if defined, cannot be a rotation other than through a multiple of 2. © 1994 The American Physical Society.