I argue that the best spacetime setting for Newtonian gravitation (NG) is the curved spacetime setting associated with geometrized Newtonian gravitation (GNG). Appreciation of the ‘Newtonian equivalence principle’ leads us to conclude that the gravitational field in NG itself is a gauge quantity, and that the freely falling frames are naturally identified with inertial frames. In this context, the spacetime structure of NG is represented not by the flat neo-Newtonian connection usually made explicit in formulations, but by the sum of the flat connection and the gravitational field.
2Newtonian Gravity: The Orthodox Approach
3Newtonian Gravity: Additional Symmetries
5A Newtonian Equivalence Principle: Inertial Frames in Newtonian Gravitation