Existence of families of spacetimes with a Newtonian limit

J"urgen 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 $1\mathrm{/}{c}^2$, 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 $\text{ep}=\sqrt{\lambda }$, frame theory provides a framework to study the Newtonian limit $\text{ep}\searrow 0$ (i.e. $c\to \mathrm{\infty }$). A number of ideas relating to frame theory that were introduced by J"urgen 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 J"urgen’s work.