Cauchy hypersurfaces as levels of time and temporal functions
نویسندگان
چکیده
Given any (topological) Cauchy hypersurface S of a globally hyperbolic spacetime, we construct a smooth function τ : M → R such that the levels St = τ (t), t ∈ R satisfy: (i) S = S0, (ii) each t ∈ R\{0} is a (smooth) spacelike Cauchy hypersurface. If S is also acausal (and not only achronal) then the smooth function τ becomes a time function, i.e., it is strictly increasing on any future-directed causal curve. If S is spacelike, then the time function τ can be chosen as a temporal function, i.e. a smooth function with past-directed timelike gradient everywhere.
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