Approximation of the FE feat. loose notation

[Spinny]

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 $$G$$, 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.

 

[pervect]

Cooperstock & Tiu's paper has been criticized by other authors, such as

This paper by Vogt and Letelier

While Cooperstock and Tiu continue to defend their paper, I personally think it's badly flawed, i.e. I agree with Vogt et al. Some other past threads on the general topic of this paper are:

https://www.physicsforums.com/showthread.php?t=103248
https://www.physicsforums.com/showthread.php?t=96935

As far as their notation goes, my impression was that they were basically doing a taylor series expansion of the metric in terms of some small paramter, so G(n) should be just a n'th order Taylor series approximation to the actual function that represents G. I'd have to look at the paper to refresh my memory. Unfortunatlely my browser isn't cooperating at the moment, perhaps a reboot will fix the problem.