Abstract
A new characterization for global hyperbolicity is given. The concept of cosmological time function and its regularity was considered by Anderson et al. [“The cosmological time function,” Class. Quantum Grav. 15, 309 (1998)]10.1088/0264-9381/15/2/006 and it was proved that if the cosmological time function of (M, g) is regular then it is globally hyperbolic. In this paper it is proved that if (M, g) is globally hyperbolic then there is a smooth function Ω > 0 such that the cosmological time function of (M, Ωg) is regular. It is also proved that the cosmological time function of Friedman-Robertson-Walker spacetime ((a, b) × f H, −dt2 + f h), a, b < ∞, is regular and in addition the regularity of cosmological time function for this kind of spacetimes is stable in \documentclass[12pt]{minimal}\begin{document}$\rm {Lor}(\it M)$\end{document} Lor (M).
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