Smooth cosmic censorship

Details Smooth cosmic censorship Smooth cosmic censorship

2012-01-29

arxiv.org/abs/1201.6070v1

Mathematics

Geometric Topology

4 pages

Scientific paper

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 $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the product of a closed oriented 3-manifold $N$ and $\R$ and admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to $N\times \R$. Thus one may speak of a censorship imposed by the global hyperbolicty assumption on the possible smooth structures on $(3+1)$-dimensional spacetimes.

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