The Motion of a Body in Newtonian Theories

TL;DR

This paper demonstrates that a theorem analogous to one in General Relativity also applies in Newtonian gravitation, showing inertial motion can be derived from core principles in both theories.

Contribution

It extends a known theorem about geodesic motion from General Relativity to Newton-Cartan theory, establishing a similar foundational result.

Findings

Inertial motion in Newtonian gravitation can be derived from fundamental principles.

A theorem analogous to Geroch and Jang's in GR holds in Newton-Cartan theory.

Inertial motion is a consequence of the theory's core principles in both frameworks.

Abstract

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense in which the geodesic principle has the status of a theorem in General Relativity (GR). Here we show that a similar theorem holds in the context of geometrized Newtonian gravitation (often called Newton-Cartan theory). It follows that in Newtonian gravitation, as in GR, inertial motion can be derived from other central principles of the theory.