  The most widely discussed chronology protection theorem/no-go result  for time machines in the context of classical general relativity  theory is due to Hawking (1992a). Before stating the result, note  first that, independently of the Einstein field equations and energy  conditions, a partial Cauchy surface \(\Sigma\) must be compact if its  future Cauchy horizon \(H^+ (\Sigma)\) is compact (see Hawking 1992a and Chrusciel and Isenberg 1993). However, it is  geometrically allowed that \(\Sigma\) is non-compact if  \(H^+ (\Sigma)\) is required only to be compactly  generated rather than compact. But what Hawking showed is that this  geometrical possibility is ruled out by imposing Einstein’s field  equations and the weak energy condition. Thus, if \(\Sigma_0\) is a partial Cauchy surface representing the situation just before or just as the would-be Thornian time machine is switched on, and if a  necessary condition for seeing a Thornian time machine at work is  that \(H^+ (\Sigma_0)\) is compactly  generated, then consistently with Einstein’s field equations and the  weak energy condition, a Thornian time machine cannot operate in a  spatially open universe since \(\Sigma_0\) must be compact.