Talk:Exact solutions in general relativity

message: I've renamed the page 'exact solutions' to 'Exact solutions of Einstein's field equations' as was requested and agreed upon by several editors. --- Mpatel 11:29, 12 Jun 2005 (UTC)
thread_title:  Rename 

message: For anyone interested in such things, I've created a page on the Segre classification of rank two symmetric tensors and on the Petrov classification of the Weyl tensor. ---Mpatel 17:37, 14 Jun 2005 (UTC)
thread_title:  Segre and Petrov classifications 

message: I've just added much new discussion, (too many?) more examples, citations, and I've reorganized everything.
I left the material on the Ricci decomposition (into Weyl tensor, and the fourth-rank thingies built form Ricci scalar and trace-free Ricci tensor respectively), but think it should be moved to an new article on decompositions of the Riemann tensor, which would also include the even more useful Bel decomposition.
I would like to remove the citation to Adler et al., since I think this is superceded by the new citations, which are specific to exact solutions.
The section on "difficulties" omits some issues.  Once articles on the full suite of fluid solutions and so forth are available, possibly examples should move to these articles as appropriate.  Or maybe not?
There is an urgent need for a local structure versus global structure article.  Also articles on energy conditions, congruences, closed timelike curves, completely solvable, inverse scattering transform.
: Good reorganisation. 
:I suppose it could be argued that there are too many solutions listed - although I have no objection. 
:Agree with the comment about moving the Riemann tensor decomposition to another article, regarding which, I think EMS and myself agreed that a discussion of the Riemann tensor decomposition (and it's physical interpretation - 'Riem = Weyl + Ricci') would be good; it might also link in nicely to the Segre and Petrov classifications.
:I was gonna mention the 'fluid' issue (including more general fluids), but I think you implicitly covered that in your comments above. I wrote down the energy-momentum tensor for a general fluid some weeks ago (see that article). Maybe an article (or a section in an article) on fluid solutions would be good: the fluid solutions could be mentioned there.
:I changed some words like 'horrendously' and 'damn' to less POV (point of view) words. Although I agree completely with what you said, I think such words are perhaps too emotive in a wikipedia article. :) 
: There is actually a short article on closed timelike curves, although it's called closed timelike curve. I was gonna start an article on the energy conditions, but given the fact that different authors mean different things when they talk about the strong, weak and dominant energy conditions, I eventually chickened out of creating such an article. Maybe an authority like Wald should be used regarding such terminology (or even better, whoever first used the terms, 'strong energy condition', etc..., and then say that some authors have varying terminology). ---Mpatel 17:05, 23 Jun 2005 (UTC)
thread_title:  Major Rewrite 

message: Because after several weeks I just could not internalize the tongue-twisting "Exact solutions to Einstein's field equations":
* Einstein's or Einstein?
* equations or equation?
* solutions of or solutions to?
This article now shares the same name as new subcategory, in parallel with "Coordinate charts in general relativity" and other new subcategories I introduced earlier today.
I have returned from my Wikivacation and am beginning by adding some of the missing articles on exact solutions.  Since I seem to have become artificially hung up on designing an "equationbox" in advance of writing articles, I have decided to write some articles first and use the experience to design the equation boxes.  Again, the idea is to have templates for "standard information" such as:
* a line element with range of coordinate variables
* definition of a frame (four orthonormal vectors, one timelike and three spacelike),
* list of generators of the Lie algebra of Killing vectors,
* presentation of a timelike congruence and its expansion and vorticity,
* presentation of null congruence and its optical scalars,
* presentation of Riemann curvature in Bel decomposition (wrt a frame).
---CH  (talk) 08:52, 27 July 2005 (UTC)
thread_title:  New Name 

message: Created the article tetrads in general relativity. There does not appear to be a sufficiently good article on tetrads in WP (the closest one is Cartan connection applications, but it's yucky), so the new article should start pretty much from the basics. After that, the idea was to give an example or more of the use of tetrads (see sections 3 and 4 of this page). --Mpatel 14:41, 28 July 2005 (UTC)
replies: text: I think that the best generalization of tetrads is "frame fields" ("tetrads" are very often "triads"). As such Frame fields in general relativity is a good name. Maybe this name can be shortened to just Frame field because I don't see this term used in a topic other than relativity. Lantonov (talk) 09:59, 4 August 2018 (UTC)
thread_title:  Tetrads in general relativity 

message: Hi CH. I've changed the link 'local structure' to 'local spacetime structure' (same for global). I think this is a little clearer and will avoid potential ambiguities with any other articles that have a similar local/global structure demarcation like local/global structure of ... , hmmm let's see, ... the countryside. Anyway, I think you get my point and hope you agree that this change is ok. These new links are also to be found at spacetime, which also needs a little tidying up.--Mpatel 16:00, 31 July 2005 (UTC)
replies: text: Yes, this sounds like a good idea to me too.  By the way, I am planning to move the fluids to "fluid solution" article, and so forth, once I get these written.  I forgot to say I plan to very shortly write an article on "static spherically symmetric perfect fluid solutions", since these are very important, and there have recently been some interesting developments which render them MUCH more tractable!---CH  (talk) 02:18, 1 August 2005 (UTC)
thread_title: Local/global spacetime structure

message: Hi Chris. Where's the new article on 'Ricci decompositions' ? ---Mpatel  (talk) 07:17, August 11, 2005 (UTC)
:Try using "Go" rather than "Search" in the sidebar at the left of your browser window.  And it's called "Ricci decomposition".  I just tested this and "Go" works for me. I think the server is having a hard time keeping the searchable database up to date.---CH  (talk) 09:09, 11 August 2005 (UTC)
thread_title:  Ricci decompositions article ? 

message: The present state of this article suggests where I plan to expand on the themes introduced very sketchily here.  Solution methods and especially symmetries and solution generating methods (Baecklund transformation like methods) deserve their own articles, and I hope to write them. Ditto for existence and linear/nonlinear stability.  But I'll probably first try to write articles bluing most of the red links referring to articles on particular exact solutions which have yet to be written.  That will probably require writing articles on various coordinate charts.  I think there is a steep curve here: I am going slower than I would like because so much of the background is missing.  I wanted to write the article on Robinson-Trautman spacetimes today, but got bogged down in writing the articles on electrovacuum solution, etc., rewriting this one, writing biographies related to these, etc.  But as more and more of these background articles get written, at least as stubs, the other articles will probably come faster and faster.---CH  (talk) 09:14, 11 August 2005 (UTC)
thread_title:  Future plans, redux 

message: I think the theme of this article should be the interplay between specific exact solutions like de Sitter lamdavacuum, or families of solutions like Robinson-Trautman, Ernst vacuums, with work on the solution space itself, particularly questions of existence, uniqueness, and stability.  I haven't yet been able to bring this out at all, but hope to do so in future rewrites.  A major goal should be to put the RT vacuums, de Sitter lambdavacuum, T3 Gowdy vacuums, etc., in perspective by explaining background for general results and then in individual articles on these solutions, briefly explaining major results such as the recent proof of cosmic censorship for the above mentioned Gowdy vacuums, spikes, and so forth.  Similarly, I am still trying to get to the RT vacuum article, in which I hope to explain the connection with Calabi flow and thus with Calabi-Yau manifolds; the goal is to make it appear natural that Richard Schoen's resolution of the Yamabe problem used ideas from tools developed in the context of gtr, and going the other way, David Maxwell has applied the Yamabe number to existence of solutions in gtr.  And of course RT vacuums are much "in the news" lately regarding new analysis of outgoing radiation and asymptotic approach to de Sitter.
We will need articles on all of the following (no particular order):
*Dimension counting (get some handle on how tiny our families of known solutions are, compared to the entire solution space),
*Existence and uniqueness of solutons (huge subject, so could easily develop into a set of pages),
*"Minisuperspaces" from families of solutions, applications of dynamical systems theory to perturbations within the family, Lyapunov stability of flows (ditto), 
*Nonlinear global stability theorems,
*Initial-value formulations,
*ADM mass,
*quasilocal energy-momentum,
*gravitational energy-momentum complexes,
*much improved stress-energy tensor article,
*energy conditions,
*positive energy theorem,
*Bianchi classification, with individual articles (the one on Type IX will be most important for Mixmaster, NUT, rotating cosmologies, etc.),
*Similarity conjecture (B. J. Carr),
*Weyl curvature conjecture (Penrose),
*Penrose inequalities (stronger than positive energy theorems),
*BKL conjecture,
*Classification of singularities (scalar, nonscalar, strong, weak; simple explicit examples given in pp wave articles),
*Cauchy horizons,
*Event horizons,
*Smoothness issues in gtr (c.f. impulsive waves, nonunique extensions),
*Mixmaster models.
Each of these should cite the original paper, the best recent paper(s) giving most relevant latest theorem(s), and the best available review, if any is known.  Note that I have been using existing templates to make the appearance of the pages more uniform.
The article as I have rewritten it to date already segues into (for example) a more specialized articles on fluid solutions, which should eventually segue into an article on static spherically symmetric perfect fluids, which should link to articles on the solution schemes and perhaps to some individual articles on say the Schwarzschild fluid, the Buchdahl theorem, etc.  Hopefully anyone wishing to help out will understand my intent of a hierarchical descent into more and more detailed articles.
Articles yet to be written on some exact solutions which are particularly important in connection with the big picture in say the review by Friedrich, include:
*NUT vacuum,
*RT vacuums < RT null dusts < RT spacetimes (three increasingly specialized articles),
*dS lambdavacuum (merge two existing articles into this),
*T3-Gowdy vacuum < Gowdy vacuum (related to CPW and also to important stuff in Friedrich's review). 
Hopefully, it will be possible to gracefully inform the reader that the higher articles slur over many important points (e.g. in my first attempt at a very rough account of basic facts about the solution space in this article, I only mentioned two groups of equations for initial value formulation, but really one should discuss four groups, each with their own difficulties and partial resolutions).
Also, I am not trying to write a review article myself; the idea is not to cite everything, just to cite the most useful reviews or, in the most detailed articles, to cite the really key papers as well as the best specialized reviews available.---CH  (talk) 23:20, 11 August 2005 (UTC)
thread_title:  Theme of this article 

message: The section on 'Constructing solutions' seems very large. How about chopping down this section to a paragraph or two and sending the rest of that section to a new article solution generating methods (general relativity) (or a similar title) ? This would also fit in nicely with trying to organise the mathematics of general relativity article, where I believe a link to an article like the one I just proposed would be better. Comments ?---Mpatel  (talk) 10:16, 11 October 2005 (UTC)
thread_title:  New article on 'solution generating methods (GR)' 

message: I'm a newbie to higher mathematics and I wonder, when you say that something (such as solving an equation) is "difficult", what does that mean? That it's impossible? Possible only in certain circumstances? Always possible but time-consuming? Some clarification would be welcome. Meneth 14:35, 16 June 2006 (UTC)
replies: text: By 'difficult', we mean theoretically possible, but any standard techniques to solve equations are not particularly helpful. Hence, new techniques have to be found - or the old ones can be used but would be very time-consuming. Hope that clarifies some things. Cheers. MP   (talk) 17:10, 16 June 2006 (UTC)
thread_title:  "Difficult" 

message: I have extensively edited earlier versions of this article, which concerns a topic particularly dear to my heart, and I had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article to its fate.
Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive.  I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.
Good luck in your search for information, regardless!---CH 23:27, 30 June 2006 (UTC)
thread_title: Students beware

message: This article relies so heavily on advanced physics terminology that I have severe problems understanding it.  I have marked it as confusing.  Could someone rewrite this so that at least the introduction will make sense to the average reader?  Dr. Submillimeter 21:05, 17 March 2007 (UTC)
replies: text: Email me (see my user page) if you want to learn more about the now defunct WikiProject GTR.  Our work was not without flaw, and it was left incomplete once we quit WP in despair, but we actually tried hard to write articles which would be comprehensible to a variety of audiences, taking as our model the best of John Baez's expositions. ---CH 07:02, 7 August 2007 (UTC)
thread_title:  Clean-up needed (Confusing text) 

message: I'd like to suggest that this article be merged with Solutions of the Einstein field equations. There doesn't seem to be enough difference in scope to warrant two articles.TimothyRias (talk) 14:18, 30 November 2010 (UTC)
thread_title:  Suggested merge 

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message: is Schwarzschild solution an exact solution? Jackzhp (talk) 16:29, 3 April 2019 (UTC)
replies: text: Yes, of course. It is the second known exact solution after Minkowski space. JRSpriggs (talk) 08:25, 4 April 2019 (UTC)
thread_title: Schwarzschild solution