Relativity from the Geometrization of Newtonian Dynamics

TL;DR

This paper geometrizes Newtonian dynamics under a generalized inertia principle, deriving a metric that reproduces classical gravitational effects and extends gravitoelectromagnetism to multiple sources, bridging Newtonian and relativistic descriptions.

Contribution

It introduces a geometric framework for Newtonian dynamics that reproduces general relativity results and extends gravitoelectromagnetism to complex source configurations.

Findings

Derives a metric matching Schwarzschild in the static case

Reproduces classical tests of General Relativity

Extends gravitoelectromagnetism to multiple sources

Abstract

Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize Newtonian dynamics for any conservative force. For an object moving in a spherically symmetric force field, using a variational principle, conservation of angular momentum and a classical limit, we construct a metric with respect to which the object's worldline is a geodesic. For the gravitational field of a static, spherically symmetric mass, this metric is the Schwarzschild metric. The resulting dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and exactly reproduces the classical tests of General Relativity. The metric of gravitoelectromagnetism is extended to handle a gravitational field generated by several sources.