  We investigate a generalization of the so-called metric splitting of globally
hyperbolic space-times to non-smooth Lorentzian manifolds and show the
existence of this metric splitting for a class of wave-type space-times. Our
approach is based on smooth approximations of non-smooth space-times by
families (or sequences) of globally hyperbolic space-times. In the same setting
we indicate as an application the extension of a previous result on the Cauchy
problem for the wave equation.
