Existence of families of spacetimes with a Newtonian limit

Details Existence of families of spacetimes with a Newtonian limit Existence of families of spacetimes with a Newtonian limit

2009-08-19

arxiv.org/abs/0908.2832v1

Gen.Rel.Grav.41:2093-2111,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1007/s10714-009-0843-5

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 $1/c^2$, 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 $\ep=\sqrt{\lambda}$, 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 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.

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