Abstract
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.
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Communicated by P. Chrusciel
This work was partially supported by a grant from the Simons Foundation (# 235674 to Vladimir Chernov).
The second author was supported by grants from DFG and RFBR.
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Chernov, V., Nemirovski, S. Cosmic Censorship of Smooth Structures. Commun. Math. Phys. 320, 469–473 (2013). https://doi.org/10.1007/s00220-013-1686-1
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DOI: https://doi.org/10.1007/s00220-013-1686-1