Existence of families of spacetimes with a Newtonian limit

@article{Oliynyk2009ExistenceOF,
  title={Existence of families of spacetimes with a Newtonian limit},
  author={Todd A. Oliynyk and Bernd Schmidt},
  journal={General Relativity and Gravitation},
  year={2009},
  volume={41},
  pages={2093-2111}
}
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… 
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