  There are two sources of doubt about the effectiveness of Hawking’s  no-go result even for open universes. The first stems from possible  violations of the weak energy condition by stress-energy tensors  arising from classical relativistic matter fields (see Vollick 1997  and Visser and Barcelo   2000).[24]  The second stems from the fact that Hawking’s theorem functions as a  chronology protection theorem only by way of serving as a potential  no-go result for Thornian time machines since the crucial condition  that \(H^+ (\Sigma_0)\) is compactly  generated is supposedly justified by being a necessary condition for  the operation of such machine. But in retrospect, the motivation for  this condition seems frayed. As argued in the previous section, if  the Einstein field equations and energy conditions entail that all  hole free extensions of \(D^+ (\Sigma_0)\)  contain CTCs, then it is plausible to see a Thornian time machine at  work, quite regardless ofwhether or not  \(H^+ (\Sigma_0)\) is compactly generated or not. Of course, it remains to establish the existence of cases where  this entailment holds. If it should turn out that there are no such  cases, then the prospects of Thornian time machines are dealt a  severe blow, but the reasons are independent of Hawking’s theorem. On the other hand, if such cases do exist then our conjecture would be  that they exist even when some of the generators of  \(H^+ (\Sigma_0)\) come from singularities  or infinity and, thus, \(H^+ (\Sigma_0)\) is not compactly   generated.[25] 