On the existence of smooth Cauchy steep time functions
arXiv:1601.05932 · doi:10.1088/0264-9381/33/11/115001
Abstract
A simple proof is given that every globally hyperbolic spacetime admits a smooth Cauchy steep time function. This result is useful in order to show that globally hyperbolic spacetimes can be isometrically embedded in Minkowski spacetimes and that they spit as a product. The proof is based on a recent result on the differentiability of Geroch's volume functions.
Latex2e, 4 pages