# A Weyl-Type Theorem for Geometrized Newtonian Gravity

- Publication Year:
- 2015

- Repository URL:
- http://philsci-archive.pitt.edu/id/eprint/11769

- Author(s):

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##### preprint description

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.