Talk:Einstein field equations

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Contents 1 Notation change? 2 Cleaning up needed ? 3 edits made 4 Exact solutions discussion 5 teleparallelism 6 nonlinearity of EFE 7 vacuum solutions 8 Tetrad section 9 Franklin Felber? 10 Reasons for tag 11 Requested move 11.1 Discussion 12 More general intro ? 13 Solutions of the EFE 14 Other uses of the term ? 15 edits by Allen McC. 16 Vandalism 17 what were the basic assumptions? 18 Matter models 19 Derivation of Newton's law 20 Sign conventions 21 History

[edit] Notation change?

I propose that the notation should be changed in the article to reflect more standard usage in the field. In particular, spacetime indices should be greek letters, and the Einstein tensor should have the letter G, instead of E

Comments? Lethe 22:13, Jun 16, 2004 (UTC)

I think that many people nowadays use Latin letters for spacetime indices (although a lot of people still use Greek). I think that for consistency's sake, as well as keeping up to date with most research papers, it's better to use Latin letters for spacetime indices.

Totally agree with the comment about the Einstein tensor (I made the new change).

I think that the article is inappropiately using Wald's abstract index notation, where tensors are denoted by G_{ab} (with subindices a,b,c,d...) , and the subindices do not indicate the component of the tensor but rather the rank of the rank of the tensor. G_{ab} represents the tensor itself, and not its components. Tensor components are still indicated by Greek letters, G_{\mu\nu}. Many research papers use Wald notation. So I propose:

• Either to use the abstract index notation adequately (and explaining it),

• Or to work in components, as traditional, and thus change the indices from ab to \mu\nu (or ij).

--Daniel Arteaga 12:31, 28 Mar 2005 (UTC)

That last comment has clarified a few things. I would prefer to use Wald's abstract index notation. Let's try this approach with proper explanation.

[edit] Cleaning up needed ?

I think this article could do with some cleaning up.

(1) The notation change has been mentioned.

(2) Is the section on 'tensor geometry' needed ? (should it be in another article ?).

(3) The section on solutions of the field equations should surely come after the section on the field equations themselves.

(4) Perhaps a qualitative discussion of the initial value problem should be included.

That's all I can think of just now.

[edit] edits made

moved discussion of exact solutions to page on exact solutions. Mpatel 17:32, 6 Jun 2005 (UTC)

[edit] Exact solutions discussion

Lethe -

In dicussing the solutions of the EFE, the new text is much more correct than the older one you reverted to. Also, the exact solutions are of secondary importance here. Mpatel has moved them to a new page, with an updated explanation of what an exact solution is. I for one approve of this organization, but just as importantly I approve of what he is saying in the editted pages.

At the least, if you think that the exact solutions belong in the EFE page then kindly make your case for that here first. Then if we decide that it is proper one of us will merge the pages back together. In the meantime, I repeat that I highly approve of the totality of Mpatel's edits: What is written about EFE solution, both in general and of the exact kind, is a wast improvement over the previous text. At the least, that older text should be kept in the history were it belongs.

--EMS | Talk 18:44, 6 Jun 2005 (UTC)

Apologies for not fully explaining (here) why I moved that chunk of text on exact solutions. I was doing a lot of chopping and changing and must have forgotten to explain it here. I was also worried that some1 might revert my edits, but I'm glad that at least 1 person approves of them. Mpatel 11:11, 8 Jun 2005 (UTC)

Firstly, let me say that I mostly reverted because I thought I saw a fairly large deletion, without edit summary, and just assumed it was a mistake. If I had known that it was intentional, I would not have reverted. So I apologize for that misunderstanding.

But now that I bring my attention to it, I don't really agree with the change. Here are my reasons:

1. exact solutions of einsteins equations are probably the most important results of the theory, and at least some of them (and why not a list of all of them?) should be here
2. the text in question is actually quite short. it's just a list with a very short summary and separate link to each solution. if the list of solutions is nothing more than a list, why should it warrant its own article?
3. the new article has a wrong name. exact solutions?? That's far too specific! Do you envision eventually including exact solutions to Navier-Stokes, Yang-Mills, the Klein-Gordon equation, and Maxwell's equations, all in one place? What about the rest of the diff eqs? I suppose this objection could be easily laid to rest by renaming the article exact solutions to the Einstein field equations or some such.
4. the link is not prominently displayed enough. as I mentioned earlier, this is a very important part of the theory. It should have its own section, and if there is so much to write on the subject, then a subpage should be made, and linked prominently from the top of the summary in the main page, as is always done in featured articles.

Basically, I think I could be happy with the way things are, if we still had the list of exact solutions, with a 5 word commentary on each solution, along with two sentences about the general principles of exact solutions, and a link to a (properly renamed) subarticle. the subarticle would then have detailed information about the methods of finding exact solutions. maybe a synopsis of the solution for each guy in the list. well... I'm dreaming.

Anyway. I think the move could be good in the long run, might not be so good now, but whatever, as long as it wasn't a weird deletion, I don't care. The text is still somewhere, and is linked to from this article. I didn't realize that at the time, and that is reason enough to revert my undeletion. -lethe ^talk 12:53, Jun 8, 2005 (UTC)

I agree with you that the "exact solutions" article should be renamed. I can also agree that some coherent discussion of solutions of the EFE should be in this page. Indeed, solving the EFE in general needs to be discussed.

My big reason for being vehement on keeping the changes is that exact solutions of the EFE are not "physically realizable" solutions as the old text claimed. Instead they are a subset of the EFE whereby a metric tensor can be formulated with an Einstein tensor that is equal to the stress-energy of the spacetime in question. Some exact solutions (such as the Alcubierre metric) may not be physically realizable. (The Alcubierre metric uses negative energy, whetever that is and if it even is.) At the same time, other cases lacking exact solutions (such as two bodies orbiting each other) are quite obviously not just physically realizable but physically realized.

So overall you have some good thoughts here. All I ask is that their implementation be done in a way that moves the article forwards.

--EMS | Talk 14:56, 8 Jun 2005 (UTC)

In making the edits, I was thinking long term. The articles exact solutions (ES) and Einstein's field equation are quite short at the moment and they will no doubt be expanded in the future (for example, in ES, I was thinking of perhaps including descriptions of various techniques used in searching for exact solutions of EFE - Petrov types, Segre types etc.).

I agree that some of the exact solutions could be mentioned in the EFE article, but they should definitely be mentioned in ES - the problem/question then becomes: 'is it OK to have that same list on both pages ?' Certainly, a handful of the important ones could be mentioned in passing on the EFE page but a more complete list should be in ES. I don't think there is much point in listing all the known exact solutions (Kramer, Stephani et al have done that).

Agree about the name change for ES.

Mpatel 16:51, 8 Jun 2005 (UTC)

Mpatel - I think that you are on the right track with these thoughts. "'[I]s it OK to have the same list on [multiple] pages?'" To me it depends on the size of the list and its importance to the article(s). However, in general the answer would be "No". Some overlap is needed to relate the pages, but their covering the same ground to a large extent often is troublesome. (For example, before you fixed it the EFE and math-of-GR pages disagreed as to what an "exact solution" is. [I was about to fix that myself, but you beat me to it.]) So I approve of your idea of listing some important metrics here, while keeping the full list in the exact solutions page.

We may also want to consider having the subarticle be on solutions instead of just exact solutions. However, it should be noted that exact solutions are preferred since anything odd in a non-exact solution begs the question of "is this real, or is it an artifact of the computation that would vanish if a (more) exact solution was known?".

--EMS | Talk 02:18, 9 Jun 2005 (UTC)

[edit] teleparallelism

Considering the fact that Einstein himself wrote a paper on the teleparallel formulation of gravity, I think it should stay in the article. No? -lethe ^talk 22:35, Jun 10, 2005 (UTC)

I have been looking at this, and it seems to be a failed attempt to create a unified field theory incorporating causitive mechanisms for both gravitation and electromagnetism. I will first direct you to the comment at the end of this report of Einstein's. It seems that he was having trouble generating correct equations of motion. This is only one of the reports I found on this teleparalellism web site. Overall it seems to be an effort that got dropped after 1930, and that probably says a lot about it. I have also found a 2002 newsgroup posting by Chris Hillman on this matter which leads to me believe that the theories are distinguishable. There is also an implication that the predictions become identical in the special case of no torsion, in which case the theories have become identical!

I don't know anything about teleparallelism being used to unify field theory and gravity, but it doesn't surprise me that people would try that. I mean, they tried it with GR (cf. Kaluza-Klein), and teleparallelism looks superficially more similar to field theory than GR does. For a more conservative introduction to teleparallelism (i.e. without any unification), see gr-qc/0011087. Equation 21 of that paper is the Einstein field equation in the teleparallelism formalism. My recollection is that the two theories are identity on topologically trivial spacetimes, but not necessarily so on nontrivial spacetimes. Of course, no one knows the topology of our spacetime yet, so there's no experimental reason to prefer one over the other. -lethe ^talk 02:36, Jun 11, 2005 (UTC)

Unification seems to have been Einstein's goal with this. I gather he at some point decided that he was barking up the wrong tree, and dropped it.

I also agree that there is no known experimental reason to prefer GR to teleparallelism. However, I will point out three things:

• I myself am working on a modification of GR to remove the black hole from theory. It also agrees with extant experimental results within the margins of error for the observations. However, I will not present it in Wikipedia due to its being truly original research, and its lacking any support in the field at this time.
• There is this little thing called Occam's Razor which says that when two theories give results which are in accord with observation, preference should be given to the simpler one. GR seems to be a special case of teleparallelism, and so is the simpler theory.
• Unless I am mistaken, noone has seen if teleparallelism works in the medium strength gravitational fields of the binary pulsars. This is a serious issue as the binary pulsar observations blew Rosen's bimetric theory out of the water, and have set a lower bound on the parameter ω for the Brans-Dicke scalar-tensor theory which is so large that the difference between it and GR is at best miniscule.

Einstein embraced teleparallelism as a chance to extend GR. It seems to have failed to to live up to that promise. If one cannot distinguish between the theories, then teleparallelism is useless unless you can show that it is a better fomulation of GR. On the other hand, if there is a difference, then the statement that they give the same results is false and this is an alternate theory. Either way, it does not belong here. --EMS | Talk 05:21, 11 Jun 2005 (UTC)

My impression is that this is an alternate theory, and one that is followed by a small minority of physicists and possibly not any of any standing. If you like, we can ask Chris for his opinion. (I don't want to bother him unless it is needed and will be a good use of his talents, but this issue appears to qualify on both counts.) However, mine is that it does not belong here. If it deserves mentioning then it should be done in the GR article itself in the alternate theories section or in a subarticle on alternate theories. Indeed, the Einstein-Cartan formalism (which this seems to be related to) also should not be here as I see it, but I am not yet sure of what to do with it.

Yes, teleparallelism is an alternate theory, but a viable one. It deserves a mention on wikipedia. If you argue that it should go in the GR article and not this one, I'm willing to listen to that argument (though I think it could well go in both). Maybe I agree with your argument, and then we can move it, but at the time, it looked like you were deleting, not moving, and that's why I reverted (as with MPatel's edit earlier.) -lethe ^talk 02:36, Jun 11, 2005 (UTC)

I was deleting it. I felt that it does not belong here, and still do. Yes. I think it should be moved to the GR article and listed as an alternate theory. Either that or the reference should be dropped completely. Once again, this article is about the EFE. If an alternate theory supports the EFE, it is redundent here. If it does not support the EFE, then it is irrelevant here. Either way, discussions of alternate theories belong elsewhere. So I won't touch that reference for now. I make no promises for later, or for anyone else.

BTW - I couldn't care less about whether teleparallelism is viable, and neither does Wikipedia according to the Wikipedia NPOV policy. In that policy it is stated that if only a very small part of a community supports a certain viepoint, its being covered in Wikipedia is inappropriate even if their viewpoint is correct. So don't show me the teleparallelism is viable. Instead show me that it has support in the community of physicists! --EMS | Talk 05:21, 11 Jun 2005 (UTC)

So for the moment I will leave the teleparallelism reference alone. It's having a defender is reason enough to do so for now. However, I ask you consider that for reasons of scope that it does not belong here, and that for reasons of its being followed by a very small minority of physicists may not even be appropriate to mention in Wikipedia as an alternate theory (but it may be worthy of mentioning in the development of general relativity article). --EMS | Talk 01:48, 11 Jun 2005 (UTC)

I would have to agree with EMS's view that teleparallelism is a theory and does not belong in the EFE article. I think that even a passing mention of teleparallelism's field equations are inappropriate in the EFE article, as 'EFE' is almost always taken to mean 'the field equations that Einstein wrote down in formulating GR', no mention of teleparallelism being mentioned - as EMS wrote above, teleparallelism was taken to be an extension of GR. --- Mpatel 10:30, 11 Jun 2005 (UTC)

I moved teleparallelism and  Einstein-Cartan theory to general relativity.  -lethe talk 06:57, Jun 13, 2005 (UTC)

[edit] nonlinearity of EFE

Mentioned a few things about EFE being nonlinear in the metric. I think it's ok to mention differences between EFE and other dynamical equations like Maxwell's equations (ME) and Schrodinger's equation (SE) (yes, I know there is more than 1 type of SE), as it's a pretty important mathematical difference with physical implications - of which I have yet to explore properly. ---- Mpatel 14:20, 11 Jun 2005 (UTC)

[edit] vacuum solutions

Vacuum solutions incorporated into EFE, as the vacuum field equation page seemed more like a definition rather than an article. --- Mpatel 15:45, 13 Jun 2005 (UTC)

I also had the same idea. Thanks for doing this. ---CH

[edit] Tetrad section

That 'tetrad formalism' section has been bugging me for a while now, as it didn't quite seem to fit in to the general discussion of the Einstein field equations (on the face of it, it's really got nothing to do with the field equations). Therefore I have moved it to the exact solutions page where it fits in a lot more naturally (many techniques used to obtain exact solutions, for example, employ the tetrad formalism). Hope this is ok. ---Mpatel 28 June 2005 14:01 (UTC)

[edit] Franklin Felber?

Shouldn't this claim http://www.physorg.com/news10789.html be mentioned somewhere in the article? --Gene s 07:48, 12 February 2006 (UTC)

Hold your horses :). Felber hasn't actually presented the 'solution' to the EFE. Once it's presented, we'll be better able to assess the claim that it is actually an exact solution of the field equations of general relativity. There have been claims by people of discovering an alleged solution, but which are, in fact, not (for example, the Alcubierre drive). The whole business of anti-gravity (especially antigravity in GR) is a little wild. So let's just wait and see exactly what Felber is claiming and once all the maths has been ploughed through and interpretations have been clarified, then we'll all be in a better position to assess what significance Felber's research has. However, I do agree that it is worthy of mention (whatever the outcome), but it should be mentioned in the exact solutions page, not here. MP (talk) 08:53, 12 February 2006 (UTC)

[edit] Reasons for tag

There are two problems here that need resolving:

• This article is misnamed. It should be the Einstein field equations, not Einstein's field equations Einstein's field equation.
• The introduction is in error. The field equations are a tensor expression representing up to 10 differential equations. This is mentioned in the bodu of the article, but the inconsistency between the intro and the text is not good.

The big problem with resolving the name problem is that the current redirect at Einstein field equations has to be removed before this page can be moved to that title. --EMS | Talk 05:54, 17 February 2006 (UTC)

Are you saying you think the name should be singular (equation) or plural (equations)? The singular fits better with my mathematical sensibilities, but the plural sounds better to my ears. -- Fropuff 17:33, 17 February 2006 (UTC)

I agree with EMS' first suggestion: the article should be called the Einstein field equations (most popular designation). How do we get rid of the redirect - is it simply a matter of deleting the redirect (once consensus has been reached) ? MP (talk) 18:17, 17 February 2006 (UTC)

Yes, any admin can delete the redirect and move the page if there is a consensus to do so. -- Fropuff 18:37, 17 February 2006 (UTC)

1. I have corrected my statement above. (darm those pestky "s"-es.)
2. The redirect can be removed and the rename done by using WP:RfD WP:RM.

If one of you would like to initiate the RfD move request, I would appreciate it. Otherwise I will get around it over the long weekend. --EMS | Talk 22:10, 17 February 2006 (UTC)

[edit] More general intro ?

Perhaps the introduction could be made slightly more intuitive. I can't help thinking that general readers will be turned away by the words, 'stress-energy tensor' and 'Einstein tensor'. I think what I'm saying is that there is too much technicality for the opening sentence. The article should start by generally telling the reader what the EFE describes. Also, all the definitions should be at the start. Begin quite generally, then we can get specific. I think the opening sentence should be fairly short, snappy, and intuitive with minimum technicalities.

Perhaps something like the following:

'The Einstein Field Equations (EFE) are a set of ten equations in Einstein's theory of general relativity describing the fundamental force of gravitation as a curved spacetime caused by matter and energy'. The EFE are sometimes called Einstein's equation or Einstein's equations.

'The EFE collectively form a tensor equation and equate the energy-momentum tensor (representing the sources of curvature) with the Einstein tensor (representing spacetime curvature)'.

Then keep the second paragraph of the present version. MP (talk) 12:15, 3 March 2006 (UTC)

I think that it is a good start, but you cannot use the term "energy-momentum tensor" because

1. the proper name is "stress-energy tensor", and
2. that link redirects to something called "stress tensor" which is much less then helpful.

Also, do be aware that momentum is also a source term for gravitation. So it is really four-momentum as expressed in the stress-energy tensor that is the real source of gravitation. --EMS | Talk 16:24, 3 March 2006 (UTC)

I've tried out an amalgam of our approaches to writing the introduction. Is it ok ? MP (talk) 18:06, 17 March 2006 (UTC)

[edit] Solutions of the EFE

There really needs to be an article on Solutions of the Einstein field equations, as non-exact solutions need to be discussed too. This future article could discuss solutions in general, then have a subsection on exact solutions (with a 'main article' thingy). Some techniques for finding non-exact solutions can be briefly discussed. Oh dear, that link redirects to exact solutions. We should get rid of that redirect. MP (talk) 15:52, 28 March 2006 (UTC)

I think it's a good idea to have such an article. Now we just need to find someone to write it. If someone does write it, then it makes sense to remove the redirect, but until then, it should stay. -lethe ^{talk +} 16:03, 28 March 2006 (UTC)

I'll second these views. --EMS | Talk 06:09, 29 March 2006 (UTC)

Created the new stubby article as above. MP (talk) 11:12, 16 April 2006 (UTC)

[edit] Other uses of the term ?

Should there perhaps be a mention somewhere in the article of other uses of the term EFE? - I'm just referring to the fact that in higher-dimensional theories, Einstein's field equations appear and they are still called by the same name. MP (talk) 15:43, 18 June 2006 (UTC)

I don't think there is anything in the article that is particular to 4 dimensions. -lethe ^{talk +} 16:27, 18 June 2006 (UTC)

Actually, the article mentions Einstein's theory of general relativity and that is 4-dimensional. MP (talk) 21:38, 18 June 2006 (UTC)

[edit] edits by Allen McC.

This editor is making two sets of changes. The first is changing the indices from a and b to μ and ν. I have little issue with this.

The other change is in the sign of the right hand side of the EFE. This editor claims that a negative sign is more common (and equivalent), but I rarely see that, and it was not presented that way in my GR courses at the University of Maryland. (This editor is also claiming that the two forms are equivalent, which could be the case but for which I would want documentation by an authoritative source.) I wonder if this editor is not being confused by the trace of the EFE being R = − T. --EMS | Talk 20:51, 19 December 2006 (UTC)

Ever since I came to Wikipedia, I have been trying to use the abstract index notation in most relativity articles, so I do have an issue with the first set of changes by Allen McC. As for the second set of changes (the minus sign), I must confess that I don't recall seeing the -ve sign on the RHS of the EFE too often (I think I may have seen it somewhere, but it was an old book). Usually, the RHS has a plus sign. In the university where I learned GR (in Britain), we used a plus sign. MP (talk) 22:02, 19 December 2006 (UTC)

We seem to be on the same page about the RHS sign. If this is an equivalent form, then it should be noted, but like you I have rarely seen a minus sign there. I will support you on the indexing. --EMS | Talk 22:33, 19 December 2006 (UTC)

Do a newtonian approximation of the metric g_μν = η_μν + h_μν where h is a disturbance in the flat metric eta=(-1,1,1,1). You end up with: where phi is the gravitational potential. Rewriting yields . Then you look at Poisson's equation . The stress energy tensor holds T₀₀ = ρc². Combining all that you get . That's where the form comes from, you see? I seems that eta=(-1,1,1,1) is commonly used. Weinberg uses it, Dirac uses it, some lecture pdf's use it, Misner-Thorne-Wheeler use it too. When I first derived the field equations I used η = (1, − 1, − 1, − 1) (i think adler-basin-schiffer uses this one) and got for the approximation. But when I tried to determine the constant, I just looked at the potential phi=-GM/r which goes with a minus by definition(!) and I found just another way to get the minus there. So no matter what eta you use, you end up with the minus which comes in because of the convention to write the grav. potential with a minus. I've looked though all the books and papers now and I've not yet seen another notation so it must be correct - or at least the convention that is commonly used. Hence I suggest that we use the same notation here - same applies for the indices! It is common to write μ,ν when you have 4 dimensions - in three dimensions it's common to write i,j. We should use the same notations here as those that are used in the textbooks because there is no good reason to make the equations look different; it only confuses it think. Even Einstein used μ and ν in his original papers; I just found a "-k" in his paper too and now I think I figured it out: the minus sign is part of the konstant, but it is common to write "-k" and make the constant positive, surely you can write "k" and say the minus is in there. But when you write 8piG/c^4 you should not forget the minus; I guess that's where this error comes from. --Allen McC. 23:35, 19 December 2006 (UTC)

There isn't any error in the RHS being positive. nor do I see anything in your math other than a bunch of handwaving. I am more interested in your sources as they are what matter here, but I need more explicit refereces rather than a bunch of name dropping. From what I am seeing, Ohanian uses a negative RHS while Wald and most web sites use a positive RHS. I don't see that value that you are adding to this article. --EMS | Talk 06:30, 20 December 2006 (UTC)

P.S. Rather than firghting over the sign, we need to obtain some better sense why the sign is arbitrary, or if it is not what considersations control it. That is information that should be in the article. --EMS | Talk 17:56, 20 December 2006 (UTC)

I'm backing up EMS on this one. I believe I've seen "-k", but I've never seen -8piT. The positive sign is conventional in textbooks, research literature, and on Wikipedia. Introducing confusion over the sign will not be helpful to the reader. Allen, you'll have to be much more persuasive if you want to make a substantial change like this.

P.S. I could care less about the alphabet of the indices. It was just easier to revert that way. --MOBle 22:31, 20 December 2006 (UTC)

Thanks for the support. Now I can continue to revert as needed without worrying about WP:3RR. --EMS | Talk 22:37, 20 December 2006 (UTC)

I notice that Allen is fairly new to Wikipedia, so let's try to stay cool. Allen, I hope you don't feel ganged-up-on (and please do take note of WP:3RR). The way to resolve this is to use outside sources, develop consensus here, then make any changes. For my part, all outside sources I've ever used have the positive sign, and that's how I think we should keep it.

Again, I have no issue with "ab" versus "\mu\nu", so anyone who wants to can feel free to change that part back, if you ask me. --MOBle 22:56, 20 December 2006 (UTC)

Someone was so kind to send me this link: Sign_convention, so it looks like that it's conventional - just as I said. I've had a conversation with several profs at my university and they all agreed that the minus sign is more commonly used (at least by them). Now this link tells us a lot and it seems to be an old issue. Still, the textbooks use the minus sign - I've looked though about 7 of em. Of course, the sign doesn't change the physics. So my idea was to change the formulation (indices, sign) to the formulation that is more commonly used, so that it doesn't conflict with that. It should be mentioned though, or maybe we should write something like together with a little comment on what that's all about; or we should mention the article about the sign convention. Not loosing a word on this is definately not an option. I'm gonna change it back, save for the minus. The other changes are ok I think.--Allen McC. 01:01, 21 December 2006 (UTC)

Excellent! That edit explains what I wanted explained. I took a look at Wald and Ohanian again. Sure enough, Wald is using the -+++ signature with a positive RHS, while Ohanian uses a +--- signature and has a negative RHS! I won't quibble over the tensor index notation myself, but MP does prefer the use of Wald's abstract index notation and its use of latin indices for pure tensor equations (such as the EFE). --EMS | Talk 02:22, 21 December 2006 (UTC)

I enthusiastically agree that the equation could be right if you changed the sign of the metric. The definition of the Riemann tensor would be unchanged. The Ricci tensor is one contraction of Riemann with the metric, so you would get a relative minus sign there. You get two more with the Ricci scalar times the metric. In this case, gets a relative minus sign. I also agree that the signature of the metric is entirely arbitrary.

However, I have never seen a source in General Relativity which uses the +--- signature. Particle physicists use +--- all the time, but they do Special Relativity. I've only ever read Wald and MTW as textbooks, but all the GR literature I've ever read (which is a lot) uses the -+++ convention. Also, +--- appears in no lecture notes I've taken at Caltech or the University of Chicago.

The point is: Saying +--- is "widely used in the standard textbooks" suggests that all those textbooks use that convention. I don't believe that this is true (though I don't have my books with me at the moment), and it's unnecessary at best. I'm just deleting that one sentence. --MOBle 06:10, 21 December 2006 (UTC)

I've looked though Einstein's original paper and he used η_μν = diag( − 1, − 1, − 1,1) where the time coordinate is x⁴. I've seen it in many books but I'm not sure anymore if there's a "common signature" - I think both are in use and that's it.--Allen McC. 14:23, 21 December 2006 (UTC)

-+++ is definitely the most common signature used in GR, to the point that some people claim it is a de-facto standard. +--- is used with spinors however, and I prefer it myself as it makes the invarient length squared of timelike path and the associated mass-energy sqaured positive. However, I feel that it is incumbent on us to reflect the current wisdom (or habits) in the field. Only in the lack of direction from the literature should our personal preferences be used. --EMS | Talk 15:53, 21 December 2006 (UTC)

Oh, yeah; I always forget about spinors when I'm arguing that -+++ is the way to go. +--- is okay by me (and most general relativists, it seems) only when using spinors. Consistency is something we should strive for on Wikipedia. --MOBle 15:59, 21 December 2006 (UTC)

Alright, but when you use -+++ you end up with the minus sign :) Then -k should also be more common (?) --Allen McC. 16:55, 21 December 2006 (UTC)

I'm not sure what you just said. To clarify, using results in the field equations

and you're mathematically free to swap the sign of the metric if you swap the sign on one side of the equation above. The definition and usage of "k" isn't something I'll take issue with. --MOBle 19:14, 21 December 2006 (UTC)

[edit] Vandalism

There has been a high rate of vandalism recently, specifically from Keller Dude. He should either be banned or cautioned. His behaviour has been unacceptable. —The preceding unsigned comment was added by PepperySugar (talk • contribs) 01:16, 9 February 2007 (UTC).

He was banned by Wikipedia admins a short time ago, after ignoring a number of warnings. —Krellis 01:17, 9 February 2007 (UTC)

[edit] what were the basic assumptions?

I think there were six. Obviously, one was relativity. I think it is important to give readers an idea of how the six assumptions became the EFE.CorvetteZ51 01:03, 15 February 2007 (UTC)

There are six fundamental principles listed in General_relativity#Fundamental_principles. Perhaps that is what you are thinking of. However, only a subset of these contribute to the EFE. --EMS | Talk 01:27, 15 February 2007 (UTC)

some of those six are results,not inputs. From memory, one of the other assumptions was 'Poisson's equation'. I can't find, on the internet,what I once read, that was a reasonable discussion of where the EFE came from, what I don't like about the current text is that it reads like a college textbook.CorvetteZ51 08:15, 15 February 2007 (UTC)

There are some things to be said both for and against its reading like a textbook. As for Poisson's equation, that is a starting point for the linear approximation, but is only indeirectly relevant to the EFE. Relativity requires that gravitational interacts be described with a 10-component rank-two (or symmetric) tensor. Once you toss in the requirement that gravitation be described with curvature, the stress-energy of the spacetime being a determining factor in the amount of the curvature, and the need for general covariance, you quickly arrive at a tensor expression where stress-energy is associated with a rank-two curvature expression. That is what the EFE are. --EMS | Talk 17:56, 15 February 2007 (UTC)

[edit] Matter models

Shal we add other matter models than Einstein-Maxwell equations, like elasticity, fluid, null dust, Enstein-Yang/Mills? Temur 22:18, 24 October 2007 (UTC)

Th Einstein-Maxwell equations are very common, which is why I included them here (I want to expand the section a little). I suppose that other models could at least deserve a brief mention. MP ^{(talk•contribs)} 19:53, 21 November 2007 (UTC)

[edit] Derivation of Newton's law

I've included a derivation of Newton's law of gravity in a show/hide box. I have to check the minus signs ! MP ^{(talk•contribs)} 19:48, 21 November 2007 (UTC)

The idea is good. But it's not just a minus sign. The whole section needs fixing signs, factors of two, etc. Could someone have a look at a couple of textbooks and fix it? —Preceding unsigned comment added by 83.243.113.85 (talk) 00:01, 1 April 2008 (UTC)

[edit] Sign conventions

I am not so sure, but it seems to me that in mostly plus conventions, as used in this article, the sign of the cosmological term is other then written here. i think the sign of the term is wrong in the first equation of "the cosmological constant", under "vacuum field equations" however it is correct again. (when written on the right hand side, the cosmological term should have a minus sign in mostly plus conventions, no?) could someone check this? —Preceding unsigned comment added by 140.247.123.225 (talk) 00:07, 10 March 2008 (UTC)

[edit] History

I think that a History section would be appropriate for this article, perhaps showing Einstein's route to the field equations (probably in a show/hide box). Comments ? MP ^{(talk•contribs)} 17:58, 27 February 2008 (UTC)