General Relativity and Gravitation

, Volume 41, Issue 9, pp 2093–2111

Existence of families of spacetimes with a Newtonian limit

Open AccessResearch Article

DOI: 10.1007/s10714-009-0843-5

Cite this article as:
Oliynyk, T.A. & Schmidt, B. Gen Relativ Gravit (2009) 41: 2093. doi:10.1007/s10714-009-0843-5

Abstract

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 \({\epsilon \searrow 0 \,{\rm (i.e.}\, c\rightarrow \infty)}\). A number of ideas relating to frame theory that were introduced by Jürgen have subsequently found important applications to the rigorous study of both the Newtonian limit and post-Newtonian expansions. In this article, we review frame theory and discuss, in a non-technical fashion, some of the rigorous results on the Newtonian limit and post-Newtonian expansions that have followed from Jürgen’s work.

Keywords

Frame theoryNewtonian limitPost-Newtonian expansions
Download to read the full article text

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesMonash UniversityMelbourneAustralia
  2. 2.Max Planck Institute for Gravitational PhysicsGolmGermany