Cosmic censorship of smooth structures

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.

5 pages; V.2 - title changed, minor edits, references added

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"

Cited by in corpus (6)

• Lyapounov Functions of closed Cone Fields: from Conley Theory to Time Functions
• Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
• Global solvability of the vacuum Einstein equation and the strong cosmic censorship in four dimensions
• Exotica or the failure of the strong cosmic censorship in four dimensions
• Exotica and the status of the strong cosmic censor conjecture in four dimensions
• Cauchy surfaces and diffeomorphism types of globally hyperbolic spacetimes