Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by Jürgen Ehlers)

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.

arXiv comment22 pages, 1 figure. Matches published version in the 'Golden Oldie' section of the Journal of General Relativity and Gravitation, Vol. 51

References in corpus (22)

• The Many Faces of Gravitoelectromagnetism
• The Status of Multi-Dimensional Core-Collapse Supernova Models
• Bondi-Sachs Formalism
• Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory
• Gravitational wave signatures in black-hole-forming core collapse
• Integrability of irrotational silent cosmological models
• Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects
• Equations of Gravitational Instability are Non-Local
• Axisymmetric core collapse simulations using characteristic numerical relativity
• Lagrangian theory of structure formation in relativistic cosmology I: Lagrangian framework and definition of a nonperturbative approximation
• The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System
• The topology of the universe: the biggest manifold of them all
• The sky pattern of the linearized gravitational memory effect
• Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order
• On the Newtonian Limit of the Weyl Tensor
• Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves
• Radiation Memory, Boosted Schwarzschild Spacetimes and Supertranslations
• Kerr Black Holes and Nonlinear Radiation Memory
• An exact Lagrangian integral for the Newtonian gravitational field strength
• The Bondi-Sachs metric at the vertex of a null cone: axially symmetric vacuum solutions
• Boosted Schwarzschild Metrics from a Kerr-Schild Perspective
• Existence of families of spacetimes with a Newtonian limit

Cited by in corpus (7)

• On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies
• The 1+3-Newton-Cartan system and Newton-Cartan cosmology
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Non zero Coriolis field in Ehlers' Frame Theory
• Direct correspondence between Newtonian gravitation and general relativity
• Spherically symmetric black holes and affine-null metric formulation of Einstein's equations
• Simultaneous determination of mass parameter and radial marker in Schwarzschild geometry