  We extend the argument that spacetimes generated by two timelike particles in
D=3 gravity (or equivalently by parallel-moving cosmic strings in D=4) permit
closed timelike curves (CTC) only at the price of Misner identifications that
correspond to unphysical boundary conditions at spatial infinity and to a
tachyonic center of mass. Here we analyze geometries one or both of whose
sources are lightlike.
  We make manifest both the presence of CTC at spatial infinity if they are
present at all, and the tachyonic character of the system: As the total energy
surpasses its tachyonic bound, CTC first begin to form at spatial infinity,
then spread to the interior as the energy increases further. We then show that,
in contrast, CTC are entirely forbidden in topologically massive gravity for
geometries generated by lightlike sources.
