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Cauchy surfaces in a globally hyperbolic spacetime. (English) Zbl 0644.53061
An elegant proof of the following theorem is given: A space-time (M,g) is globally hyperbolic iff a $$C^{\infty}$$ manifold $$N_ 0$$ and a diffeomorphism $$\psi$$ : $$N_ 0\times R\to M$$ exist with $$\psi (N_ 0\times \{a\})$$ being a spacelike connected Cauchy surface for all $$a\in R$$. [See also the author’s thesis (TU Berlin, 1987; Zbl 0612.53038)].
Reviewer: Bernd Wegner

##### MSC:
 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 83C75 Space-time singularities, cosmic censorship, etc.
##### Keywords:
globally hyperbolic; Cauchy surface
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##### References:
 [1] DOI: 10.1090/S0002-9904-1977-14394-2 · Zbl 0376.53038 · doi:10.1090/S0002-9904-1977-14394-2 [2] DOI: 10.1063/1.1665157 · Zbl 0189.27602 · doi:10.1063/1.1665157 [3] DOI: 10.1007/BF00759586 · Zbl 0425.53032 · doi:10.1007/BF00759586
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