Existence of families of spacetimes with a Newtonian limit

Abstract

Jürgen Ehlers developed \emph{frame theory} to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter $\lambda$, which can be thought of as $1/c^2$, where $c$ is the speed of light. By construction, frame theory is equivalent to general relativity for $\lambda >0$, and reduces to Newtonian gravity for $\lambda =0$. Moreover, by setting $\ep=\sqrtλ$, frame theory provides a framework to study the Newtonian limit $\ep \searrow 0$ (i.e. $c\to \infty$). 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.

References in corpus (3)

• The Newtonian limit for perfect fluids
• Post-Newtonian expansions for perfect fluids
• Newtonian perturbations and the Einstein-Yang-Mills-dilaton equations

Cited by in corpus (3)

• Review on Non-Relativistic Gravity
• Motion of small bodies in general relativity: foundations and implementations of the self-force
• Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by Jürgen Ehlers)