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

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

2006-12-03

arxiv.org/abs/gr-qc/0612014v3

Class.Quant.Grav.24:2781-2808,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex2e, 29 pages, 2 figures, uses psfrag package. v2: a problem with theorem 5.5, which was erroneously stated twice, and som

Scientific paper

10.1088/0264-9381/24/11/002

We 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.

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