Existence of families of spacetimes with a Newtonian limit

J??rgen Ehlers developed frame theory to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter I>, 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 I> > 0, and reduces to Newtonian gravity for I> = 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 J??rgen 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??rgena??s work.