The issue that must be faced now is what further conditions must be imposed in order that the appearance of CTCs to the future of \(\Sigma_0\) can be attributed to the operation of a time machine. Not surprisingly, the answer depends not just on the structure of the spacetime at issue but also on the physical laws that govern the evolution of the spacetime structure. If one adopts the attitude that the label “time machine” is to be reserved for devices that operate within a finite spatial