Newtonian gravitation in Maxwell spacetime

Abstract

This paper argues for the appropriateness of Maxwell spacetime as the minimal spacetime structure in which one may formulate a theory of Newtonian gravity. I begin by presenting an intrinsic characterization of Maxwell gravitation that, eschewing covariant derivative operators, makes use only of a standard of rotation and other more primitive structures. I then revisit the question of whether Maxwell gravitation and Newton-Cartan theory are equivalent, demonstrating that previous results may be extended to all but the vacuum case since candidate geometrizations are not free to vary through purely gravitational degrees of freedom. Lastly, I consider the space of possible geometrizations of Maxwell gravitation more broadly and argue for a sense in which curvature is not entirely a matter of convention in classical spacetimes.