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

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Abstract

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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Authors and Affiliations

  1. Dpto. de Geometría y Topología, Facultad de Ciencias, Fuentenueva s/n, 18071, Granada, Spain

    Antonio N. Bernal & Miguel Sánchez

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  1. Antonio N. Bernal
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  2. Miguel Sánchez
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Additional information

Communicated by G.W. Gibbons

The second-named author has been partially supported by a MCyT-FEDER Grant, MTM2004-04934-C04-01.

To Professor P.E. Ehrlich, wishing him a continued recovery and good health

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Bernal, A., Sánchez, M. Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes. Commun. Math. Phys. 257, 43–50 (2005). https://doi.org/10.1007/s00220-005-1346-1

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  • DOI: https://doi.org/10.1007/s00220-005-1346-1

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