An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture---in its usual broad formulation---is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat Lorentzian 4-manifold is constructed which is not globally hyperbolic and no perturbation of it, in any sense, can be globally hyperbolic. This very stable non-global-hyperbolicity is the consequence of our open spaces having a "creased end" i.e., an end diffeomorphic to an exotic ${\mathbb R}^4$. Open manifolds having an end like this is a typical phenomenon in four dimensions. The construction is based on a collection of results of Gompf and Taubes on exotic and self-dual spaces, respectively, as well as applying Penrose' non-linear graviton construction (i.e., twistor theory) to solve the Riemannian Einstein's equation. These solutions then are converted into stably non-globally-hyperbolic Lorentzian vacuum solutions. It follows that the plethora of va 查看全文>>