Existence of families of spacetimes with a Newtonian limit

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/c 2, 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.