Talk:Solutions of the Einstein field equations

Non-exact solutions

I think it's worth having an article on non-exact solutions. MP (talk) 16:44, 6 May 2006 (UTC)

This would be a great article to have, I myself am curious as to what the various solutions to the EFEs actually are, but if no one can list any, this article should be deleted. Sloverlord 21:13, 26 October 2006 (UTC)

I created the article to take account of the fact that there are, broadly speaking, two classes of solutions to the EFE: Exact and non-exact. The article on exact solutions is the main one, but there is (now) a stubby article on non-exact solutions (which I finally got round to creating). I think the present article should be kept, as some general info. on solutions of the equations can be dealt with, whereas the other 2 articles discuss the solutions in more detail (or will do so). There is a lot of general info. that can be included about solutions of the EFE, such as various solutions techniques (e.g. symmetry considerations), various difficulties encountered in solving the EFE and what they mean physically (e.g. nonlinearity 'means' the gravitational field can act as it's own source) and comparing these issues to other field equations (e.g. Maxwell's equations). Thanks for bringing my attention to this article, as I seem to have forgotten about it as soon as I created it ! Cheers. MP (talk) 14:35, 27 October 2006 (UTC)

German Astro Group (84.158.*.*) additions

Please stop trying to insert your material into this article. As I explained to you during your previous spam campaign, this material is biased, poorly written, and shows little in-depth knowledge of general relativity. Especially disturbing is your focus on alternate cosmologies, naming three competitors to the Friedmann-Lemaître-Robertson-Walker metric which really are not very notable, and therefore are inappropriate to an overview article such as this one. You are also doing nothing to fit your edits into the article, but given the inadequacies of the material itself that is a fairly minor concern.

If needed, this article (and others) can be semi-protected to keep you from editing it anonymously. --EMS | Talk 20:09, 3 July 2007 (UTC)

Errors and comments.

Einstein Field equation is a 6-variable PDE, not 14. You will never say, because x = y, therefore there are two unknowns x and y. The correct descriptions of the solution of EFE are:

(1) due to symmetry, DOF = 16-6 = 10

(2) due to conservation of the SE-tensor, there are 4 equation as constraint. DOF = 10-4 = 6

(3) Given SE-tensor, you need to find the metric tensor satisfying EFE, thus the independent DOF is 6.

(4) Normally it is hard to model the situation using a fully-written SE-tensor, thus modelling is required, that is why we usually use equation to state to further reduce the complexity of the SE-tensor.

Moreover, one should manage to derive some of them, especially the static case, or combine this page with that. The non-exact sol page is not suggested to shown here as the page gives readers nothing other than brief description.

Cheers,

lucarioic

Does the continuity equation follow from EFE?

Alas, I crunch a bit of math, but I know very little about physics. At a certain point the article says "To obtain solutions, the relevant equations are the above quoted EFE plus the continuity equation", but later it is asserted that "the continuity equation is a consequence of Einstein's equations." It is not possible that both statements are correct! This should be fixed. 78.15.165.142 (talk) 13:26, 31 July 2015 (UTC) PS. Why a "low importance" article?78.15.165.142 (talk) 13:29, 31 July 2015 (UTC)