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arXiv · 1510.02089

A Weyl-Type Theorem for Geometrized Newtonian Gravity

Erik Curiel
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Abstract

I state and prove, in the context of a space having only the metrical and affine structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's for a Lorentz manifold. The theorem says that a projective structure and a suitably defined compatible conformal structure jointly suffice for fixing the metric structure of a Newtonian spacetime model up to constant factors, and for fixing its affine structure as well. The theorem allows one to give a natural, physically compelling interpretation of the spatiotemporal geometry of a geometrized Newtonian gravity spacetime manifold, in close analogy with the way Weyl's Theorem allows one to do in general relativity.

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Erik Curiel. 2016-03-09. A Weyl-Type Theorem for Geometrized Newtonian Gravity. https://arxiv.org/abs/1510.02089

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