Cosmic Censorship of Smooth Structures

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard ${\mathbb{R}^4}$ . Similarly, a smooth 4-manifold homeomorphic to the product of a closed oriented 3-manifold N and ${\mathbb{R}}$ and admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to ${N\times \mathbb{R}}$ . Thus one may speak of a censorship imposed by the global hyperbolicty assumption on the possible smooth structures on (3 + 1)-dimensional spacetimes.