A Weyl-Type Theorem for Geometrized Newtonian Gravity
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I state and prove, in the context of a space having only the metrical structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's in a Lorentzian space. The theorem, loosely speaking, says that a projective structure and a suitably defined compatible conformal structure on such a space jointly suffice for fixing the metrical structure of a Newtonian spacetime model up to constant factors. It 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.