Global solvability of the vacuum Einstein equation and the strong cosmic censorship in four dimensions

Let M be a connected, simply oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put M×?M?{point}. In this paper we prove that if X× homeomorphic but not necessarily diffeomorphic to M× (more precisely, it carries structure à la Gompf) then can equipped with complete Ricci-flat Riemannian metric. As byproduct of the construction follows metric self-dual as well consequently in fact hyper-Kähler manifold. particular find largest member Gompf–Taubes radial family large exotic R4’s admits (and manifold). These solutions are converted into Lorentzian ones thereby exhibiting lot new vacuum accessible by initial value formulation. A natural physical interpretation them context strong cosmic censorship conjecture topology change discussed.