Physical obstacles to time-travel

The author critically examines the properties of geometries generated by parallel infinite cosmic strings, or equivalently point particles in 2+1 gravity, that possess closed time-like curves (CTC). It is shown that CTC are physically excluded: their existence requires that the centre of mass of the sources be tachyonic, which entails unacceptable boundary conditions, in particular presence of CTC at spatial infinity. These conclusions also hold if one or both of the sources are lightlike.