# Do superluminal worldlines constitute closed time-like curves under the right conditions?

A closed time-like curve is defined as a word-line that returns to its starting point, in the $$x$$, $$y$$, $$z$$, $$t$$ coordinates. So, for a chronology respecting observer, an object traversing a closed time-like curve would appear to violate causality. Under certain conditions (Tolman et al.), superluminal propagation of signals also appears to violate causality. Does this indicate that for a tachyonic anti-telephone situation, the worldline of a superluminal tachyon could be considered as a closed time-like curve?