Globally hyperbolic flat space-times

We consider (flat) Cauchy-complete GH space-times, i.e., globally hyperbolic flat Lorentzian manifolds admitting some Cauchy hypersurface on which the ambient Lorentzian metric restricts as a complete Riemannian metric. We define a family of such space-times-model space-times-including four subfamilies: translation space-times, Misner space-times, unipotent space-times, and Cauchy-hyperbolic space-times (the last family-undoubtful the most interesting one-is a generalization of standard space-times defined by G. Mess). We prove that, up to finite coverings and (twisted) products by Euclidean linear spaces, any Cauchy-complete GH space-time can be isometrically embedded in a model space-time, or in a twisted product of a Cauchy-hyperbolic space-time by flat Euclidean torus. We obtain as a corollary the classification of maximal GH space-times admitting closed Cauchy hypersurfaces. We also establish the existence of CMC foliations on every model space-time. (C) 2004 Elsevier B.V. All rights reserved.