Eisenhart's theorem and the causal simplicity of Eisenhart's spacetime

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dc.creatorMinguzzi, E.
dc.date2006-12-03
dc.date2007-04-23
dc.date.accessioned2026-07-07T10:37:06Z
dc.date.available2026-07-07T10:37:06Z
dc.descriptionWe give a causal version of Eisenhart's geodesic characterization of classical mechanics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction, pp-waves). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is shown in detail, and in particular it is proved a one-to-one correspondence between Newtonian frames and Abelian connections on suitable lightlike principal bundles. The relation of Eisenhart's theorem in the lightlike case with a Fermat type principle is pointed out. The operation of lightlike lift is introduced and the existence of minimizers for the classical action is related to the causal simplicity of Eisenhart's spacetime.
dc.descriptionLatex2e, 29 pages, 2 figures, uses psfrag package. v2: a problem with theorem 5.5, which was erroneously stated twice, and some misprints have been fixed, v3: change of definition of function I in theorem 5.5
dc.identifierhttps://arxiv.org/abs/gr-qc/0612014
dc.identifierhttp://arxiv.org/abs/gr-qc/0612014
dc.identifierClass.Quant.Grav.24:2781-2808,2007
dc.identifierdoi:10.1088/0264-9381/24/11/002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180266
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleEisenhart's theorem and the causal simplicity of Eisenhart's spacetime
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