On Gravitational Energy in Newtonian Theories

There are well-known problems associated with the idea of gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation. We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.