# Existence of families of spacetimes with a Newtonian limit

@article{Oliynyk2009ExistenceOF, title={Existence of families of spacetimes with a Newtonian limit}, author={Todd A. Oliynyk and Bernd Schmidt}, journal={General Relativity and Gravitation}, year={2009}, volume={41}, pages={2093-2111} }

Jürgen Ehlers developed frame theory to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter λ, which can be thought of as 1/c2, where c is the speed of light. By construction, frame theory is equivalent to general relativity for λ > 0, and reduces to Newtonian gravity for λ = 0. Moreover, by setting $${\epsilon=\sqrt{\lambda}}$$ , frame theory provides a framework to study the Newtonian limit $${\epsilon \searrow 0 \,{\rm (i.e…

## 6 Citations

Editorial note to: On the Newtonian limit of Einstein’s theory of gravitation (by Jürgen Ehlers)

- PhysicsGeneral Relativity and Gravitation
- 2019

We give an overview of literature related to Jurgen Ehlers’ pioneering 1981 paper on Frame theory—a theoretical framework for the unification of general relativity and the equations of classical…

The Newtonian limit of geometrostatics

- Mathematics, Physics
- 2011

The Newtonian limit of General Relativity for static isolated systems with compactly supported matter is discussed, new quasi-local notions of mass and center of mass are introduced, and several uniqueness claims in geometrostatics as well as other geometric and physical properties of these systems are proved.

Motion of small bodies in general relativity: Foundations and implementations of the self-force

- Physics
- 2010

Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme…

On slowly rotating axisymmetric solutions of the Einstein-Euler equations

- Mathematics, PhysicsJournal of Mathematical Physics
- 2018

In recent works we have constructed axisymmetric solutions to the Euler-Poisson equations which give mathematical models of slowly uniformly rotating gaseous stars. We try to extend this result to…

Singular perturbation techniques in the gravitational self-force problem

- Mathematics
- 2010

Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this…

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