Communications in Mathematical Physics
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 Comm. Math. Phys., 2013, Volume 320, Issue 2, Pages 469–473 (Mi cmph7)

Cosmic censorship of smooth structures

V. Chernova, S. Nemirovskibc

a Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, NH 03755, USA
b Steklov Mathematical Institute, 119991 Moscow, Russia
c Mathematisches Institut, Ruhr-Universität Bochum, 44780 Bochum, Germany

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.

 Funding Agency Grant Number Simons Foundation 235674 Deutsche Forschungsgemeinschaft Russian Foundation for Basic Research 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.

DOI: https://doi.org/10.1007/s00220-013-1686-1

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Accepted:23.09.2012
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