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Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime

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arxiv 2303.05941 v1 pith:ONFVLIF3 submitted 2023-03-10 gr-qc math.APmath.DG

E. Minguzzi This is my paper · ORCID
classification gr-qcmath.APmath.DG
keywords lorentzianminkowskispacetimemanifoldsproperlyembeddableisometricallyadvantage
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I characterize the Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime (i.e. the Lorentzian submanifolds of Minkowski spacetime that are also closed subsets). Moreover, I prove that the Lorentzian manifolds that can be properly conformally embedded in Minkowski spacetime coincide with the globally hyperbolic spacetimes. Finally, by taking advantage of the embedding, I obtain an infinitesimal version of the distance formula.

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