  Thus, we propose that one clear sense of what it would mean for a Thornian time machine to operate in the setting of general relativity theory is given by the following assertion: the laws of general relativistic physics allow solutions containing a partial Cauchy surface \(\Sigma_0\) such that no CTCs lie to the past of \(\Sigma_0\) but every extension of \(D^+ (\Sigma_0)\) satisfying ________ contains CTCs (where the blank is filled with some “no hole” condition). Correspondingly, a proof of the physical impossibility of time machines would take the form of showing that this assertion is false for the actual laws of physics, consisting, presumably, of Einstein’s field equations plus energy conditions and, perhaps, some additional restrictions as well. And a proof of the emptiness of the associated concept of a Thornian time machine would take the form of showing that the assertion is false independently of the details of the laws of physics, as long as they take the form of local conditions on \(T_{ab}\) and \(g_{ab}\).