Faster than light motion does not imply time travel
  Seeing the many examples in the literature of causality violations based on faster-than- light (FTL) signals one naturally thinks that FTL motion leads inevitably to the possibility of time travel. We show that this logical inference is invalid by demonstrating a model, based on (3+1)-dimensional Minkowski spacetime, in which FTL motion is permitted (in every direction without any limitation on speed) yet which does not admit time travel. Moreover, the Principle of Relativity is true in this model in the sense that all observers are equivalent. In short, FTL motion does not imply time travel after all. 
H. Andr\'eka and J. X. Madar\'asz and I. N\'emeti and M. Stannett and   G. Sz\'ekely
gr-qc math-ph math.LO math.MP