Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime
General Relativity and Quantum Cosmology
2023-06-13 v1 Analysis of PDEs
Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2303.05941,
title = {Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime},
author = {E. Minguzzi},
journal= {arXiv preprint arXiv:2303.05941},
year = {2023}
}
Comments
22 pages, 1 figure