Editorial Note to : On the Newtonian Limit of Einstein’s Theory of Gravitation (by Jürgen Ehlers) Article - 2019

Thomas Buchert, Thomas Mädler

Thomas Buchert, Thomas Mädler, « Editorial Note to : On the Newtonian Limit of Einstein’s Theory of Gravitation (by Jürgen Ehlers)  », Gen.Rel.Grav., 2019, p. 162

Abstract

We give an overview of literature related to Jürgen 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.

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