Our aim is to give a simple characterization of the class of Lorentzian manifolds which can be isometrically embedded in Lorentz-Minkowski $L^N$ for some large $N$ (in the spirit of classical Nash theorem) and, then, to show that this class includes the most relevant type of relativistic spacetimes, i.e., the globally hyperbolic ones. This last result was claimed by CJS Clarke (1970), but his proof was affected by the so-called folk problems of smoothability in Lorentzian Geometry. These problems will be specially discussed.
The talk is based in a joint work with O. Müller