Lorentzian manifolds isometrically embeddable in L^N

Details Lorentzian manifolds isometrically embeddable in L^N Lorentzian manifolds isometrically embeddable in L^N

2008-12-23

arxiv.org/abs/0812.4439v4

Mathematics

Differential Geometry

Final version with minor modifications, to appear in Trans. AMS. 13 pages, 1 figure, latex

Scientific paper

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.

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