  We characterize those spacetimes which admit a isometric (or conformal)
embedding in some Lorentz-Minkowski space L^N. In particular, any globally
hyperbolic spacetime can be isometrically embedded in L^N. This is proven by a
result of its own interest: the construction of a smooth time function whose
gradient is bounded away from zero -and, thus, an orthogonal global splitting
of the spacetime with bounded lapse. The role of the so-called "folk problems
on smoothability" is stressed.
