Strong cosmic censorship and topology change in four dimensional gravity

Abstract

A physical interpretation of the recently discovered vast class of vacuum space-times, which stably violate the strong cosmic censor conjecture (in its usual broad formulation) in four dimensions, is exhibited. Namely, by elementary Morse theory we demonstrate that these geometries describe transitions between topologically different spacelike hypersurfaces. More precisely, in these four dimensional smooth vacuum space-times there exist three dimensional spacelike hypersurfaces which display an increasingly violent unbounded oscillation between topologically different closed, orientable three-manifolds as one moves towards the asymptotic region in their ambient space-times. Moreover this spatial oscillation appears as a cosmological redshift for late time observers. Therefore these new vacuum solutions shed some light onto the deep dynamic regime of general relativity and the structure of the four dimensional continuum itself. This picture, beyond offering a physical clarification how global hyperbolicity breaks down in these solutions, is also consistent with the fact that the Riemannian counterparts of these Lorentzian vacuum geometries are not only Ricci-flat but even self-dual four-manifolds hence give rise to gravitational instantons. Consequently the role of these Riemannian solutions is similar to that of Yang--Mills instantons in semi-classical non-Abelian gauge theories over Minkowski space-time.