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.

 

[Entropia]

Based on the information provided, it seems that the authors are using a "loose notation" to refer to a simplified or approximate version of the Einstein field equations. This type of approximation is commonly used in the field of general relativity, where the full equations can be quite complex and difficult to solve. By using a "loose notation," the authors are likely simplifying the equations in order to make them more manageable for their specific application.

This type of approximation is not a standard linear approximation, which means that it cannot be solved using traditional methods such as Taylor series or other mathematical techniques. Instead, it likely involves making certain assumptions or simplifications in order to reduce the complexity of the equations.

Unfortunately, without more specific information about the paper or the authors' methods, it is difficult to provide a more detailed explanation or recommend specific literature on the subject. However, a good starting point would be to look into the field of numerical relativity, which focuses on using numerical methods to solve complex equations in general relativity. This may provide some insight into the types of approximations and techniques used in this field. Additionally, reaching out to the authors directly or consulting with a professional relativist may also be helpful in gaining a better understanding of their approach.