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**Approximation of the FE feat. "loose notation"**

I'm looking for a (professional) relativist to help me clarify something. I refer to the article

*General Relativity Resolves Galactic Rotation Without Exotic Dark Matter*by Cooperstock and Tieu, available here: http://arxiv.org/abs/astro-ph/0507619v1.

They talk about the Einstein field equations to order [tex]G[/tex], and list them without any more details except a footnote stating that it's a "loose notation favored by many relativists".

I was wondering if anyone here are familiar with such an approximation scheme and could elaborate on how one goes about making such approximations, or perhaps refer me to some litterature on the subject.

Finally let me just specify that these approximations are not your standard linear approximations, and I can't seem to find any similar procedures in any textbooks (although that may just be because I'm not looking in the right books or at the right places in the books).

Thanks.