Rigid motions and generalized Newtonian gravitation. Lost in Translation

TL;DR

This paper develops a unified Newtonian framework for inertia and gravity, aiming to bridge towards general relativity, and explores the non-relativistic limit of Einstein's equations within this context.

Contribution

It introduces a generalized Newtonian theory with an equivalence principle and derives its connection to Einstein's equations in the non-relativistic limit.

Findings

Unified description of inertia and gravity in Newtonian theory

Formulation of an equivalence principle for the generalized theory

Derivation of Einstein's equations' non-relativistic limit

Abstract

We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence principle for this generalized Newtonian theory. Finally we find the non-relativistic limit of the Einstein's equations for the space--time metric derived from the Newtonian theory.