Talk:Mathematics of general relativity/Archive 1

message: I think we should use the abstract index notation (AIN) for tensors consistently on the GR pages. Previously, I wrote things like, '...the metric tensor components are g_{ab}...', but now I believe that we should make it a standard for the GR pages to use the AIN. I hope we can reach a quick consensus (in the positive) on this point. ---Mpatel  (talk) 12:33, August 14, 2005 (UTC)
: I certainly can go along with it.  However
:# This is a point that should be covered in standards for Chris' Wikiproject GTR, and
:# It is not fair to others to ask for this until it is fully explainted in the abstract index notation article. 
: So this is a good idea, but I think that you are ahead of things a bit. --EMS | Talk 04:46, 19 August 2005 (UTC)
thread_title:  Abstract index notation 

message: I have inserted a space between the Tba and the trailing comma because it made the formula look like it was a prime insted of a. Unfortunately, now the line is broken and the comma shows up first character of the new line. Can someone who knows how to insert a non-break space please fix this? Thanks. 84.160.232.20 06:35, 10 September 2005 (UTC)
thread_title:  Editing formulas 

message: Substituted at 15:21, 1 May 2016 (UTC)
thread_title: Assessment comment

message: I've just made some major revisions to the article. I intend to keep as much of EMS' work as possible, as it's all essential. Just need to work around it. A few things:
* I've included some physical reasons for choosing manifolds as the 'basis' for the maths of GR. 
* Still need stuff on tangent spaces and more on tensor and vector fields.
* I'll leave the high-powered maths of fibre bundles, spinors etc. for others (Chris ?) to deal with, but I'll create the sections and write a few words to get started. 
* I think some more on the topology of manifolds should be included.
* Some info. on (covariant and Lie) derivatives + explanation of why partial derivatives are inadequate. For Lie derivatives, the intimate connection with vector fields needs discussion; then this needs to be linked with local 1-parameter diffeo.'s. 
* Tonnes of references and reliable external links (both these should be easy).
I think I underestimated the magnitude of this major revision task! Comments welcome. ---Mpatel  (talk) 15:09, 17 September 2005 (UTC)
replies: text: You (MP and EMS) have probably noticed that I've been working recently on some mathematical background stubs (e.g. kinematic decomposition of timelike unit vector fields).  I plan to edit Energy conditions and some other articles on MP in near future, also to try to create new stubs on the Riemann tensor in gtr and on the meaning of the EFE.  Regarding the latter, some of this might eventually be merged with existing articles, but in light of the recent problems with wikiservice (MUUUUCH better in last few days!), I am thinking there might be a good point to having more short articles viz. fewer but very long articles.  Short articles are easier to create and organize, and we are less likely to encounter inadvertent edit conflicts.  Does anyone know what the accepted wisdom is vis a vis whether many short articles or few long articles are best for wikiservers, especially in the case of articles containing a good deal of LaTeX style pseudocode?---CH  (talk) 00:45, 20 September 2005 (UTC)
replies: text:  First of all, presentation should be the first consideration here.  Wikiserver considerations should come afterwards.  However, I would think that shorter articles would be better for the servers too.  --EMS | Talk 16:16, 20 September 2005 (UTC)
thread_title:  Mpatel's major revision 

message: I just added a few random items off the top of my head.  From the rapidly growing length of this list (which is not yet comprehensive), I draw the conclusion that this article must focus on trying to orient the befuddled newbie by describing in nontechnical terms the 'big picture', and sending him/her to specialized articles for more detail.  
Instead of offering a long long list of references in this article, it might be best to link to the graduate textbook and special topics sections of General relativity resources, and mention that we intend that all specialized articles will eventually contain appropriate references.---CH  (talk) 23:46, 21 September 2005 (UTC)
thread_title: To do list

message: Hi, just notice this new eprint discussing influence of gtr on differential geometry.---CH  (talk) 23:36, 28 September 2005 (UTC)
thread_title:  Possibly useful eprint

message: I've decided to combine the two sections on (affine) connections and covariant derivatives, as they are intimately connected (no pun intended). I'd like some feedback on this please. ---Mpatel  (talk) 15:23, 25 September 2005 (UTC)
thread_title:  Covariant derivatives and affine connections  

message: Again, some feedback on this would be appreciated. Maybe we can get some of the hardcore maths buffs here - maybe User: Tosha - to help us write something on Lie dragging in the Lie derivative page. ---Mpatel  (talk) 11:42, 1 October 2005 (UTC)
thread_title:  Lie derivatives 

message: I've tried to include some intuition about the linearity property of tensors. ---Mpatel  (talk) 11:42, 1 October 2005 (UTC)
thread_title:  Tensors in GR 

message: Created the page Riemann tensor (general relativity). Can dump (and organise) any relevant technical details in this new page.---Mpatel  (talk) 10:25, 8 October 2005 (UTC)
thread_title:  Riemann tensor 

message: Just created a new article: Variational methods in general relativity. ---Mpatel  (talk) 08:33, 8 October 2005 (UTC)
thread_title:  Lagrangians 

message: Mpatel -
I have given the article a once-over per your request.  There are two items that I uncomfortable with.  The first is your description of a tensor in the section Tensors in GR.  I cannot see how that introduction communicates what a tensor is or how it is used.  That equation looks correct, but the indexing is unwieldy, and you do not explain what T is.  I would advise looking at Wald pp. 20-22 for an example of a more coherent description.
The second item is your description of the covariant derivative.  You need to tell people what \Gamma/connections are before then.
Overall, it is good to see this article being taken well beyond where I left it.  I think that you pretty much have a good overview of the subject in place.  However, I very much advise being sure that you have the basics firmly in place and leave the more obtuse materials for other articles in the hierarchy.  Be advised that my concerns with the GR pages are becoming less ones of making sure that the material is correct and reasonably complete and more ones of seeking to have the material be organized and accessible based on what is in the article and/or the articles that are being linked to.  As you continue to edit this article please keep in mind that a correct but unintelliable article is no better than an incorrect but understandable one.  (This is not to say that this article is curently unintelligable, but rater that that concern is the reason for my comments above.) --EMS | Talk 03:12, 14 October 2005 (UTC)
thread_title:  Analysis of edits 

message: I plan to reduce this section slightly, once the article spacetime has enough details. Also need to mention the local isometry problem in here somewhere (and the Cartan-Karlhede algorithm). ---Mpatel  (talk) 15:26, 14 October 2005 (UTC)
thread_title:  Spacetime as a manifold 

message: It is absolutely essential to somewhere discuss the evolution equation which explains how mass/momentum indirectly creates long-range gravitational interaction.  That is, the EFE says that the immediate presence of mass/momentum in some region causes Ricci curvature there, but we need to explain how Ricci curvature causes Weyl curvature.  In particular, in the course of concentrating matter to form the Sun, we move stuff around which causes gravitational radiation and gradually curls up the vacuum surrounding the increasingly dense concentration of matter.  Roughly speaking.  See my little essay on the RelWWW website.---CH  (talk) 18:20, 18 October 2005 (UTC)
thread_title:  EFE 

message: Ok, I've been slaving away at this article for about a month and I feel burned out. I've removed the cleanup tag as I think the article has been sufficiently 'cleansed'. The inuse tag has been removed as I plan to stay away from this article for a while (I've been looking at it for too long). 
I also feel as though I've been hogging this article, so feel free to make any edits you (CH and EMS ?) think are appropriate. Please bear in mind that a lot of time has gone into rewriting the article, so I'd suggest making any major edits judiciously - or discuss these first. Of course, the article still needs a lot of content to be mentioned (see the todo list - I've just added a few more things on this list) as well as external links and references, but some of the stuff on the 'pending task' list will inevitably be mentioned elsewhere (for example, infinitesimal holonomy groups - too technical to even be mentioned in this article). Enjoy...
So, now I can start exploring some of the other GR pages... ---Mpatel  (talk) 14:10, 21 October 2005 (UTC)
replies: text: You've done some great work!  I'll try to work up the courage to assess how to continue, and I'll ask you before I make major changes.  ---CH  (talk) 18:35, 21 October 2005 (UTC)
replies: text: Thanks.  Just a point about the 'Why tensors ?' section at the start. I felt that an explanation of why tensors are used in relativity should be given straight away. I did elaborate on this justification later ('Tensors in GR'), so I don't mind if a mini-merger is done here. ---Mpatel  (talk) 08:28, 22 October 2005 (UTC)
thread_title:  Burnout 

message: An anon using IP 141.155.124.124 added the following to this and to General relativity:
On February 11, 2006, noted physicist Dr. Franklin Felber announced a new exact solution to the Einstein field equations. His new solution takes into account the gravitational field of a mass moving close to the speed of light, which has never been done before. His research shows that a mass moving faster than 57.7% of the speed of light (approximately 1.731 x 10^{8} m/s) will generate a narrow antigravity beam in front of it, thereby gravitationally repelling other masses lying in its immediate path. The greater the velocity of the mass, the stronger the force of the beam. Dr. Felber believes that his new solution can revolutionize space travel, predicting the possibility of a payload to be transported at a sufficient percentage of the speed of light by the end of the century.
This apparently refers to an eprint I must have missed, .  (Felber's affiliation is given as Physics Divsion, Starmark in San Diego, which might raise a few eyebrows; a minute with Google fails to clarify whether this "Starmark" is the same as a similarly named real estate company in that area, but with more effort this can no doubt be determined.)  Needless to say, this kind of "announcement" of an unpublished (and possibly controversial!) eprint is utterly unacceptable in an encyclopedia!
 
I haven't had a chance to look at the eprint yet, which dates from May, but I noticed right away that the claim that this alleged solution takes into account the gravitational field of a mass moving close to the speed of light, which has never been done before suggests a profound ignorance of the literature; see Aichelburg-Sexl_ultraboost and citations therein.  This is not a good sign, but I'll keep an open mind until I look at the eprint. ---CH 03:34, 14 February 2006 (UTC)
thread_title: Felber vandal

message: I've come back to this article again. This time, I'm more interested in the organisation and how it relates to content. For example, I've just added a handful of 'main article' links. This is to reduce the content in this article that is (possibly) repeated (or explained better) in another article. Related to this, affine connection is currently a stub and some of the work in 'maths of GR' could be transferred to that stub. MP   (talk) 18:14, 17 February 2006 (UTC)
thread_title:  Perspective on article 

message: This article concerns a topic 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.
I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.
Good luck to User:Mpatel and to all students searching for information, regardless!---CH 02:02, 1 July 2006 (UTC)
thread_title: Students beware

message: May I suggest that the new subsection on Solving the Einstein field equations be moved to the article solutions of the Einstein field equations, as it clearly belongs there and fits in better over there than it does here. The current article is supposed to be an overview of the maths of GR. Thanks. MP   (talk) 22:16, 23 January 2007 (UTC)
thread_title:  Suggestion for recently added subsection 

message: From the talk page of the "introduction" article (Talk:Introduction to mathematics of general relativity#The header), there seemed in June of last year to be a reasonable consensus to merge the articles, but this wasn't actioned.  I've therefore started the formal procedure, which will result in the articles being merged by default in two weeks (or sooner if consensus develops here).  I agree with the participants on the "introduction" talk page that the main article is, in fact, a great deal more accessible to the non-technical reader, and I don't expect that there's going to be a lot of actual content that needs merging. Tevildo (talk) 15:03, 13 January 2008 (UTC)
thread_title:  Merge proposal 

message: This article is currently under discussion at Wikipedia:Editor assistance/Requests#Math of General Relativity and page swap D O N D E groovily Talk to me 16:31, 25 September 2010 (UTC)
thread_title:  Editor Assistance