  Are there "no hole" conditions which show the proposed concept of a time machine is not empty? Let \(J^+(p)\) designate the causal future of \(p\), defined as the set of all points in \(\mathcal{M}\) which can be reached from \(p\) by a future-directed causal curve in \(\mathcal{M}\). The causal past \(J^-(p)\) is defined analogously. Now, we say a spacetime \((\mathcal{M},g_{ab})\) is J closed if, for each \(p\) in \(\mathcal{M}\), the sets \(J^+(p)\) and \(J^-(p)\) are topologically closed. One can verify that J closedness fails in many artificially mutilated examples (e.g. Minkowski spacetime with one point removed from the manifold). For some time, it was thought that a time machine existed under this no-hole condition (Manchak 2011a). But this turns out to be incorrect; indeed a recent result shows that any J closed spacetime \((\mathcal{M},g_{ab})\) of three dimensions or more with chronology violating region \(V \neq \mathcal{M}\) must be strongly causal and therefore fail to have CTCs (Hounnonkpe and Minguzzi 2019). Stepping back, perhaps there are other no-hole conditions which can be used instead to show that the proposed concept of a time machine is not empty. But even if such a project were successful, Manchak (2014a, 2019) has shown that the time machine existence results can be naturally reinterpreted as “hole machine” existence results if one is so inclined. Instead of assuming that spacetime is free of holes and then showing that certain initial conditions are responsible for the production of CTCs, one could just as well start with the assumption of no CTCs and then show that certain initial conditions are responsible for the production of holes. Given the importance of these no hole assumptions to the time machine advocate, much recent work has focused on whether such assumptions are physically reasonable in some sense (Manchak 2011b, 2014b). This is still an open question.