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Editorial note to: On the Newtonian limit of Einstein’s theory of gravitation (by Jürgen Ehlers). (English) Zbl 1437.83009
Summary: We give an overview of literature related to J. Ehlers’s pioneering 1981 paper [“Über den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie”, in: J. Nitsch (ed.) et al., Grundlagenprobleme der modernen Physik. Mannheim: Bibliographisches Institut. 65–84 (1981); Gen. Relativ. Gravitation 51, No. 12, Paper No. 163, 20 p. (2019; Zbl 1437.83013)] 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.

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
53Z05 Applications of differential geometry to physics
Full Text: DOI
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