  The would-be time machine operator need not capitulate in the face of Krasnikov’s theorem. Recall that the main difficulty in specifying the conditions for the successful operation of Thornian time machines traces to the fact that the standard form of causal determinism does not apply to the production of CTCs. But causal determinism can fail for reasons that have nothing to do with CTCs or other acausal features of relativistic spacetimes, and it seems only fair to ensure that these modes of failure have been removed before proceeding to discuss the prospects for time machines. To zero in on the modes of failure at issue, consider vacuum solutions \((T_{ab} \equiv 0)\) to Einstein’s field equations. Let \((\mathcal{M}, g_{ab})\) and \((\mathcal{M}', g'_{ab})\) be two such solutions, and let \(\Sigma \subset \mathcal{M}\) and \(\Sigma ' \subset \mathcal{M}'\) be spacelike hypersurfaces of their respective spacetimes. Suppose that there is an isometry \(\Psi\) from some neighborhood \(N(\Sigma)\) of \(\Sigma\) onto a neighborhood \(N'(\Sigma ')\) of \(\Sigma '\).  Does it follow, as we would want determinism to guarantee, that \(\Psi\) is extendible to an isometry from \(D^+ (\Sigma)\) onto \(D^+ (\Sigma ')\)? To see why the answer is negative, start with any solution \((\mathcal{M}, g_{ab})\) of the vacuum Einstein equations, and cut out a closed set of points lying to the future of \(N(\Sigma)\) and in \(D^+ (\Sigma)\).  Denote the surgically altered manifold by \(\mathcal{M}^*\) and the restriction of \(g_{ab}\) to \(\mathcal{M}^*\) by \(g^*_{ab}\). Then \((\mathcal{M}^*, g^*_{ab})\) is also a solution of the vacuum Einstein equations. But obviously the pair of solutions \((\mathcal{M}, g_{ab})\) and \((\mathcal{M}^*, g^*_{ab})\) violates the condition that determinism was supposed to guarantee as \(\Psi\) is not extendible to an isometry from \(D^+ (\Sigma)\) onto \(D^+ (\Sigma^*)\). It might seem that the requirement, contemplated above, that the spacetimes under consideration be maximal, already rules out spacetimes that have “holes” in them. But while maximality does rule out the surgically mutilated spacetime just constructed, it does not guarantee hole freeness in the sense needed to make sure that determinism does not stumble before it gets to the starting gate. That \((\mathcal{M}, g_{ab})\) is hole free in the relevant sense requires that if \(\Sigma \subset \mathcal{M}\) is a spacelike hypersurface, there does not exist a spacetime \((\mathcal{M}', g'_{ab})\) and an isometric embedding \(\Phi\) of \(D^+ (\Sigma)\) into \(\mathcal{M}'\) such that \(\Phi(D^+ (\Sigma))\) is a proper subset of \(D^+ (\Phi(\Sigma))\). A theorem due to Robert Geroch (1977, 87), who is responsible for this definition, asserts that if \(\Sigma \subset \mathcal{M}\) and \(\Sigma ' \subset \mathcal{M}'\) are spacelike hypersurfaces in hole-free spacetimes \((\mathcal{M}, g_{ab})\) and \((\mathcal{M}', g'_{ab})\), respectively, and if there exists an isometry \(\Psi : \mathcal{M} \rightarrow \mathcal{M}'\), then \(\Psi\) is indeed extendible to an isometry between \(D^+ (\Sigma)\) and \(D^+ (\Sigma ')\). Thus, hole freeness precludes an important mode of failure of determinism which we wish to exclude in our discussion of time machines. It can be shown that hole freeness is not entailed by maximality.[19] And it is just this gap that gives the would-be time machine operator some hope, for the maximal CTC-free extensions produced by Krasnikov’s construction are not always hole free (Manchak 2009b). But Krasnikov (2009) has shown that the Geroch (1977) definition is too strong: Minkowski spacetime fails to satisfy it! For this reason, alternative formulations of the hole-freeness definition have been constructed which are more appropriate (Manchak 2009a, Minguzzi 2012). 