Mueller, O. and Sanchez, M. (2011) LORENTZIAN MANIFOLDS ISOMETRICALLY EMBEDDABLE IN L-N. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363 (10). pp. 5367-5379. ISSN 0002-9947,
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In this article, the Lorentzian manifolds isometrically embeddable in L-N (for some large N, in the spirit of Nash's theorem) are characterized as a subclass of the set of all stably causal spacetimes; concretely, those which admit a smooth time function tau with vertical bar del tau vertical bar > 1. Then, we prove that any globally hyperbolic spacetime (M, g) admits such a function, and, even more, a global orthogonal decomposition M = R x S, g = -beta dt(2) + g(t) with bounded function beta and Cauchy slices. In particular, a proof of a result stated by C.J.S. Clarke is obtained: any globally hyperbolic spacetime can be isometrically embedded in Minkowski spacetime L-N. The role of the so-called "folk problems on smoothability" in Clarke's approach is also discussed.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GLOBALLY HYPERBOLIC SPACETIMES; RIEMANNIAN MANIFOLDS; CAUCHY HYPERSURFACES; TIME FUNCTIONS; THEOREM; CAUSAL; Causality theory; globally hyperbolic; isometric embedding; conformal embedding |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 May 2020 06:09 |
| Last Modified: | 29 May 2020 06:09 |
| URI: | https://pred.uni-regensburg.de/id/eprint/20080 |
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