Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by J\"urgen Ehlers)

TL;DR

This paper reviews J"urgen Ehlers' 1981 Frame theory, which unifies General Relativity and Newtonian gravitation, showing how Einsteinian solutions converge to Newtonian solutions in a specific limit and exploring modern implications.

Contribution

It provides an overview of Ehlers' Frame theory, highlighting its role in unifying Einstein's and Newton's gravitation and its modern applications in cosmology and initial data formulation.

Findings

Einstein solutions converge to Newtonian solutions as the causality constant approaches zero.

Frame theory reveals Maxwell-type equations underlying Newtonian gravitation.

Implications for Newtonian cosmology and light cone initial data are discussed.

Abstract

We give an overview of literature related to J\"urgen Ehlers' pioneering 1981 paper on Frame theory--a theoretical framework for the unification of General Relativity and the equations of classical Newtonian gravitation. This unification encompasses the convergence of one-parametric families of four-dimensional solutions of Einstein's equations of General Relativity to a solution of equations of a Newtonian theory if the inverse of a causality constant goes to zero. As such the corresponding light cones open up and become space-like hypersurfaces of constant absolute time on which Newtonian solutions are found as a limit of the Einsteinian ones. It is explained what it means to not consider the `standard-textbook' Newtonian theory of gravitation as a complete theory unlike Einstein's theory of gravitation. In fact, Ehlers' Frame theory brings to light a modern viewpoint in which the `standard' equations of a self-gravitating Newtonian fluid are Maxwell-type equations. The consequences of Frame theory are presented for Newtonian cosmological dust matter expressed via the spatially projected electric part of the Weyl tensor, and for the formulation of characteristic quasi-Newtonian initial data on the light cone of a Bondi-Sachs metric.