  As for the third condition—a causally innocuous past—the  question of the possibility of operating a device that produces CTCs  presupposes that there is a time before which no CTCs existed. Thus,  Gödel spacetime, so beloved of the time travel literature, is  not a candidate for hosting a Thornian time machine since through  every point in this spacetime there is a CTC. We make this third  condition precise by requiring that the spacetime admits a global time slice \(\Sigma\) (i.e., a spacelike hypersurface without   edges);[9]  that \(\Sigma\) is two-sided and partitions   \(\mathcal{M}\) into three parts—\(\Sigma\) itself, the part of   \(\mathcal{M}\) on the past side of \(\Sigma\) and the  part of   \(\mathcal{M}\) on the future side of  \(\Sigma\)—and that there are no CTCs that lie on the past side of \(\Sigma\). The first two clauses of this requirement together entail  that the time slice \(\Sigma\) is a partial Cauchy surface,  i.e., \(\Sigma\) is a time slice that is not intersected more than once  by any future-directed timelike   curve.[10] 