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arXiv · 0908.2832

Existence of families of spacetimes with a Newtonian limit

Todd A. Oliynyk·Bernd Schmidt
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Abstract

Jürgen Ehlers developed \emph{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 $\ep=\sqrtλ$, 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 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.

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Todd A. Oliynyk, Bernd Schmidt. 2009-08-19. Existence of families of spacetimes with a Newtonian limit. https://doi.org/10.1007/s10714-009-0843-5

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