# Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes

@article{Bernal2005SmoothnessOT, title={Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes}, author={Antonio N. Bernal and Miguel Grau S{\'a}nchez}, journal={Communications in Mathematical Physics}, year={2005}, volume={257}, pages={43-50} }

The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M, g) admits a smooth time function whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting if a spacetime M admits a (continuous) time function t then it admits a smooth (time) function with timelike gradient on all M.

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