Talk:General relativity/Archive 10

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Predictions/Applications

Resolved

I was thinking about doing some work on the current section "Predictions of general relativity" – rewriting, adding references and stuff like that. However, since that would also involve some re-structuring, about which there should naturally be some consensus, I'm bringing this up here on the talk page first. Instead of the current single section about predictions, I would like to introduce the following structure:

One section "Observational tests"; the focus here would be on the predictions that follow directly from the theory (without further input); differently put: these are the classical ways of putting gr to the test (gravitational frequency shift, time delay, bending of light, perihelion advance, geodetic precession, frame-dragging).

In addition, there would be a section "Astrophysical applications" which would focus on those applications where you are not only testing general relativity, but some models built on that theory – put differently, the focus would be on the role of general relativity as an important theoretical tool in astrophysics. This section would have sub-sections on gravitational lensing, on black holes, gravitational waves, and cosmology.

Of course, the division is not always clear-cut – when in doubt, I would follow the usual way this is done in textbooks (with binary pulsars included under the heading of gravitational waves, although you could make a case that this is a direct prediction). But this new division would certainly correct something that I perceive to be a weakness in the current version, namely that there is no distinction between direct predictions and more complex models, and hence no clear statement of gr's important role for astrophysics – reading this text, no-one would get an idea of the huge amounts of work going on regarding black holes and gravitational waves, for instance. Markus Poessel 19:45, 11 July 2007 (UTC)

Remember that there are other articles on black holes, gravitational waves and such which cover them in more detail. So we do not need to duplicate that here — just give a quick summary and a link to the main article. JRSpriggs 04:03, 12 July 2007 (UTC)

I'm just a beginner, but I don't see a qualitative difference between the direct predictions and the indirect, with the exception of cosmology (which I haven't read up on yet). For example, the existence of gravitational waves follows directly from the Einstein field equations themselves; you don't need to make a "weak field" approximation or assume anything else. Similarly, gravitational lensing per se follows directly from the bending of light, no? And aren't "black holes" just a consequence of the Schwarzschild metric, in the same way that, say, perihelion advance is? I agree that it would be fun to have more mathematical material to help a student eager to learn more; like, how does frame-dragging work? I just read about the Kerr metric last night before falling asleep, but it still seems mysterious. I'm trying to do my bit with the Kepler problem in general relativity, but it's still a long way from FAC. Willow 09:55, 12 July 2007 (UTC)

As I said, my main point is to make clear the difference between observations whose main function it is to serve as tests, and astrophysical applications. If you measure the light deflection close to the sun, the main goal is to put gr to the test. If you observe gravitational lenses, the main goal is to find dark matter, or to reconstruct galaxy properties, or to measure the Hubble constant - gr is used as a tool to get at something else. Gravitational waves are similar: In the simplest situation (two-body problem), you can use them to, well, prove the existence of gravitational waves and thus confirm a prediction of gr. But that's not what all but a few gravitational wave people are working on - they're trying to use gravitational waves to learn about other objects, and they do lots of modeling of gw sources in consequence. Black holes: Yes, basically a prediction of gr. But that's not what makes them so interesting - they power active galactic nuclei, people are trying to explain how they lead to jets, what their role is for the formation of the first galaxies, and so on. In all these cases, the article in its current state picks out only a very small aspect of what's important for current research. An article about gr should also reflect what people working in gr today are actually doing. In the present version, it doesn't. That's the main imbalance I'd like to address. Splitting the description into "Observations" and "Astrophysical Applications" is only one way of doing this - may be there are better ways. If we go by relative importance, then "Tests that are mainly tests" should get one section, and the important applications (Black holes, gravitational lenses, gravitational waves, cosmology) should each get their own section. I know, they do have their own articles, and I'm not saying that these separate sections should even try to approach the level of detail desirable for those separate articles. But there could be a bit more than there is now - simply so the reader of this article doesn't get a skewed impression of what's important in gr research.

Actually, re-reading what I wrote, may be that is the solution. May be the second section should be called "Research topics in general relativity". As subsections we'd have the tests, we'd have each of the topics I mentioned (plus cosmology), and we should probably add "Mathematical relativity", which is certainly under-represented (in that respect, the article is firmly stuck in the 50s). A basic structure like

1. Overview (which, frankly, should include relation to Newtonian theories and electromagnetism, since that is part of the basic structure)
2. Modern research (modern tests, black holes, gravitational waves, gravitational lenses, cosmology, search for quantum gravity, mathematical relativity)
3. History of GR
4. Alternative theories

might not be a bad way of reconciling everything that's there. Or may be it would be better for history and modern research to switch places - first history, then the present; also, the early gr predictions (which are, after all, part of the theory's historical development) could be mentioned there. And the reader would, overall, get a good overview of what those hundreds of people working in gr today are actually doing. --Markus Poessel 14:16, 12 July 2007 (UTC)

OK, that makes sense; I just hadn't understood the distinction you were making. I tried my hand at frame dragging this morning; please let me know what you think. I'll have to read up on the original papers to do better. Willow 18:09, 12 July 2007 (UTC)

I hadn't found the best way to make that distinction myself, as you can see from my evolving proposals for new structure. I think the Intro, History, Modern research structure is promising, though. As for frame-dragging: Haven't had time to look at it thoroughly, but at first glance (and off the top of my head - sorry, haven't got my references handy at the moment): Looks like a promising article; some suggestions: have a look at [1] for the history (which isn't quite right in the present version, I think); also, it would be good if we could make the distinction between Schiff effect, Lense-Thirring in the strict sense etc.; when it comes to who started Gravity Probe B, Fairbank should be mentioned; bring in Mach somewhere - show the connection to Einstein's early developments of gr; as far as lay-out is concerned, with all the multiple citations, the "Experimental tests" section looks really ugly -- if you were to change that to a Notes+References format (I know, it's tedious to make the change), that would certainly be a good deed. --Markus Poessel 19:05, 12 July 2007 (UTC)

I'll be interested is seeing how this change pans out. I had been doing a slow "prosification" of the article (moving it away from the bullet-list format that had characterized large pieces of it after I did my rewrite two years ago). I had been about to work on the "Other predictions" section, but if you are about to do your own revision of that section there is little need for me to touch it now. BTW - I do apprciate seeing others wotk on this article. I had "owned" it for some time by a kind of community default. (In essense most of the other editors were happy to follow my lead in this article.) There being new blood and enthusiasm can only be a good thing given a good grouding in the topic, respect for both Wikipedia policy and a understanding of the need to balance accuracy and accessibility in writing an encyclopedia article for a general audience. --EMS | Talk 05:02, 15 July 2007 (UTC)

Hi EMS; I'm eager to carry this forward properly by consensus (I got a bit carried away with Introduction to general relativity, but I hope it has turned out alright, even though there are objections on principle in the ongoing FAC). I'm appreciative of all the work you've been doing on relativity, and I'd greatly appreciate your feedback - should I perhaps build a sandbox? I'm not quite sure what the best overall structure for the article might be, but right now, I think

1. Overview
2. Modern research and applications
3. History of GR
4. Alternative theories

as the main sections should work best - basic ideas and formulations in the first section; black holes, grav waves, cosmology etc. in the second (but also topics like global geometry). That said, I'm not proposing to change the structure right away – writing a good section 2 (or a sandbox version thereof) would be my preferred first step. --Markus Poessel 09:17, 16 July 2007 (UTC)

OK, I've created my sandbox and have started playing. It would be kind if other editors could refrain from making major changes to the "Other predictions" section for a while; I am importing material from there into my sandbox, and a merger will be much easier if the section in the main article could stay as it is.

As you can also see, I'm still trying out what the best structure could be. At present, I favour something like

1. Overview (basic descriptions of the theory)
2. Consequences (direct consequences such as light bending, but also conceptual developments such as global geometry, horizons, singularities, gravitational waves)
3. Astrophysical applications (astrophysical role of gravitational waves, black holes as accreting objects, cosmological models)

One heartfelt plea: In re-writing the first section (time delay), I find that I can make the notes much more potentially helpful to future readers if I can use them as notes (i.e. for comments) not just as places to store the references (mentioning several references and their relation to each other in a single note, stuff like that, which gives the reader an idea of what reference will be especially useful for him or her). It would make my work much easier if we could agree to a change from a References-in-Notes format to a format with separate Notes (Comments with Harvard-like references) and References sections (full bibliographical entries). I know this involves some tedious work, but I'm willing to do that work (though all at once, but step by step). --Markus Poessel 12:50, 16 July 2007 (UTC)

(undent)If you want Harvard style ask User:KSmrq(He loves Harvard style), He knows the template very well and would be glad to help(I think).--Cronholm¹⁴⁴ 13:02, 16 July 2007 (UTC)

Thanks for the tip. My greatest worry is not the technical side, but the consensus side. I think not making the change would make what I'm trying to do significantly harder, and I'm keeping my fingers crossed that none of the editors that contribute to this article will turn out to be as passionately attached to the current reference style as I am to the separated Notes/References. --Markus Poessel 14:05, 16 July 2007 (UTC)

They will pipe up immediately if they are attached. :) I think that you won't hit too much resistance (the regulars here are reasonable, it's the IP's and cranks that insist that GR isn't real that are the problem). Let these comments sit for a while then go ahead and change if no one has an objection.--Cronholm¹⁴⁴ 14:13, 16 July 2007 (UTC)

Thanks, that sounds like good advice. Anyway, I have my sandbox to putter around in now, which makes it easier to be patient. :-) (addicted, moi?) --Markus Poessel 16:26, 16 July 2007 (UTC)

I thought I might provide some justification for the formatting I used. The headers are broadly: Intro, History, Overview, Theoretical justification, EFE, Predictions, Validity, and end-of-article-errata which I feel conveys the broad arc of the scientific method- characterize, hypothesize, predict, and verify. The justification section is (I feel) the weakest of any as one would need to address the merit and relevance of these assumptions by delving into semi-philosophical arguments about sameness/equality or observer/independence. Some of the predictions meander a little too far into describing the phenomena (which one could read by following the "main" link) rather than how GR predicts it. Likewise, as I wrote it, the verifications of various phenomena are sprinkled in with the predictions which would seem to negate the value of the Validity section (or explain why it is so stub-like). However, re-explanation of the several contexts in a later might become repetitive, thus my choice. The alternative theories under Validity likewise needs to be "paragrahized" and either briefly explicated or contextualized. Madcoverboy 21:38, 16 July 2007 (UTC)

Harvard reference style

Resolved

 – this is a reference for referencing(redundant I know...) rm only after article has stabilized

I've been asked to assist with using Harvard reference style. If you wish to do this, here's what you need to know.

• Be careful of stepping on toes. Although parenthetical names are common in the sciences, numbered superscripts are common in the humanities; this is a color/colour kind of choice, and Wikipedia is formally impartial.
• Most of the guidance can be found at WP:CITET, and at {{Citation}}.
• In the "References" section, a single template, {{Citation}}, handles everything (books, journal articles, web pages, etc.). Most of the fields are the same as {{cite book}} and the like. One important difference is the more detailed handling of author/editor names. Thus Einstein and Gravitation look like this:

  • Einstein, A. (1915), "Die Feldgleichungen der Gravitation", Sitzungsberichte der Preußischen Akademie der Wissenschaften zu Berlin: 844–847 {{citation}}: Unknown parameter |month= ignored (help)

  markup: {{citation | last=Einstein | first=A. | author-link=Albert Einstein | year=1915 | month=November | title=Die Feldgleichungen der Gravitation | journal=Sitzungsberichte der Preußischen Akademie der Wissenschaften zu Berlin | pages=844–847 | url=http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=6E3MAXK4&step=thumb }}

  • Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973), Gravitation, San Francisco: W. H. Freeman, ISBN 978-0-7167-0344-0 (See Gravitation (book).)

  markup: {{citation | last1 = Misner | first1 = Charles W. | author1-link = Charles W. Misner | last2 = Thorne | first2 = Kip S. | author2-link = Kip S. Thorne | last3 = Wheeler | first3 = John Archibald | author3-link = John Archibald Wheeler | title = Gravitation | publisher = W. H. Freeman | location = San Francisco | year = 1973 | isbn = 978-0-7167-0344-0 }} (See [[Gravitation (book)]].)

• To reference the citation from the text, use one of three templates. Each automatically generates a hypertext link based on the name(s) and date.

  • Some works on gravitation are so massive they warp spacetime themselves (Misner, Thorne & Wheeler 1973); yet Einstein (1915) presented essential equations with notable brevity. The two ingredients are the curvature tensor and the stress-energy tensor (Einstein 1915, p. 844; Misner, Thorne & Wheeler 1973, p. 41).

  markup: Some works on gravitation are so massive they warp spacetime themselves {{Harv|Misner|Thorne|Wheeler|1973}}; yet {{Harvtxt|Einstein|1915}} presented essential equations with notable brevity. The essential ingredients are the curvature tensor and the stress-energy tensor ({{Harvnb|Einstein|1915|loc=p. 844}}; {{Harvnb|Misner|Thorne|Wheeler|1973|loc=p. 41}}).

  1. For a single work with no author in the text (the most common case), use {{Harv}}.
  2. For a single work with the author named in the text, use {{Harvtxt}}.
  3. For multiple works at the same point, use explicit parens and {{Harvnb}} separated by semicolons.

In my view, footnotes and web pages make a poor user interface combination. Thus I, personally, would never use a footnote for a parenthetical remark; I would either say something in the text proper or say nothing. In kindness to readers, I would attempt to give page numbers for specific items in Gravitation. :-)

Hope this helps. --KSmrq^T 15:46, 16 July 2007 (UTC)

Hi KSmrq - many thanks, that helps indeed. For what it's worth, the kind of remark I would like to put into the notes is the kind you find in my current sandbox for this article - explanations of what aspects of the subject being referenced can be found in what form (table etc.) in what reference. --Markus Poessel 18:03, 16 July 2007 (UTC)

Merge

On Hold.

See draft page at User:Madcoverboy/Sandbox/General relativity for example of merged article. Madcoverboy 18:08, 16 July 2007 (UTC)

• Madcoverboy is too modest - he has already moved that page to general relativity. --Markus Poessel 20:04, 16 July 2007 (UTC)
  • Shucks, missed the most important one! Boldly went ahead and tried the revision on for size. Madcoverboy 20:12, 16 July 2007 (UTC)

• Oppose for now. Before we can decide whether or not a complex topic like general relativity should have an "Introduction to..." article in addition to the main article, we should be sure that it is even possible to have an excellent main article that adequately serves both potential groups of readers: Those for whom the more technical articles on relativity (which involve formulae and the appropriate higher math) are meant, and to whom the main article serves as an important turntable (mostly college students with a physics or maths connection, plus those working in the field or adjacent fields), and the "curious average person" with little interest in the mathematics for whom the article is meant to provide an easily accessible introduction. This is as good an opportunity as any to bring this article to FA status, and once we have, we can step back, look at the result and at Introduction to general relativity, and then we should have a good foundation for deciding whether or not an "Introduction to..." is needed. As for how to go about improving the article, my proposal would be to first achieve consensus on the basic structure. It's a discussion I've already started on this talk page; once we have agreement on that, we could parcel out the different sections and share the work. --Markus Poessel 20:35, 16 July 2007 (UTC)

• Oppose - I agree with Markus. Bring both articles to FA standard separately, and then step back and consider the merits of both cases. Carcharoth 22:01, 16 July 2007 (UTC)
• Oppose - there's been some considerable debate about this in the introduction's FAC nomination - suggest we wait for the result before pre-judging "what to do next". --Joopercoopers 22:32, 16 July 2007 (UTC)

• Oppose - I would like this article to be accessible to the widest audience possible, but if it is dumbed down to the point where it is accessible to people outside of the realms of physics and math then only that kind of person will benefit from it. A true GR article must describe GR as it is currenlty unserstood by the math and physics communities. Some allowance can and should made for less technical readers (since you should not have to already know GR to read this article), but it should not shy away from the core technical concepts behind the theory. OTOH, the "Intrduction" article very much is intended for a much less technical audience, givning them a feel for what GR is like and a sense of what they need to master in order to be able to handle the this article. --EMS | Talk 22:36, 16 July 2007 (UTC)
  • Withdrawn - Per Markus and Carcharoth, let's get this to FA and see how it stacks up with/against the intro article.Madcoverboy 00:09, 17 July 2007 (UTC)

Unsure of the rewrite

Unresolved

I am currently wondering if thie rewrite is worht keeping up in its current form. In the lead and what is now the justification section, there were several mistakes that I have sought to remedy. I will continue to look over this article, but I am not all that pleased with it at this time. I will admit that in terms of format and style it is an improvement, but the contents have to be accurate! My overall temptation is to do what is needed to bring this and the related articles back up to snuff in terms of technical accuracy. However, if others would like to go back to the previous version I can easily support that.

BTW - I also am not sure that I like the history being up front. I really think that the first issues to be dealt with should be the "why" and "what" of general relativity. The blow-by-blow of how it came to be is obviously notable in this context, but I don't see what is gained by covering that first. --EMS | Talk 05:50, 17 July 2007 (UTC)

I would also support going back to the pre-merger-proposal version; we should, however, in revising the article, check where the material/text currently in Introduction to general relativity might be helpful, and make liberal use of it. In other words, I support User:Madcoverboys action in principle, and I expect that in the end, a number of things he changed might end up changed in the final version in a similar fashion, but I agree that the previous version is probably a better starting point for the re-working. --Markus Poessel 06:46, 17 July 2007 (UTC)

The question of where to put the history is a question of general structure. Again, I think we should agree on the main outline before going on much further; you see from my postings above that my mind is still in a rather fluid state. The structure I prefer right now is:

1. Overview - sets out the basic structure, principles and defining concepts of the theory, culminating in Einstein's equation and the question of what a solution is.
2. Consequences of Einstein's theory (working title) - the place for the direct consequences of the theory like redshift, propagation of light, Mercury perihelion (including summaries of their observational status) and conceptual developments (causality, global geometry, horizon, gravitational waves, singularity)
3. Astrophysical applications - astrophysical black holes, search for gravitational waves and modeling of sources, cosmology, gravitational lensing
4. History
5. Alternatives

My thoughts behind this: The current "predictions" title neglects the applications/modeling aspects and thus gives a skewed impression (the great majority of people actually doing research on the subject would be surprised to find that their work should be subsumed under this heading); also, models have further input besides just gr. "Consequences" seemed a nice inclusive header, especially for later conceptual development, which should get a bit more room than they currently have. I wouldn't want to lump the astrophysical applications under "Consequences" as well, for one because it would make for widely disparate length in subsections; also, because it would again create a skewed impression (there are so many more people working on these aspects than on others that a separate section to signify weight is appropriate, I think). The only thing I do not yet like about the structure is that I don't see where quantum gravity fits in. May be, again given the sheer number of people working on this, it should get a section of its own. --Markus Poessel 08:41, 17 July 2007 (UTC)

Reverted back

I have reverted this article back to the last pre-overhaul version. I keep finding errors and misconceptions in that article which were long gone out of my version. Overall, I like the idea of moving this article beyond my organization, but I kindly request that this be done with review and consensus.

To Madcoverboy: Get with Marcus and decide how this article should look. I am happy to tighten things back up as needed.

To Marcus: The outline above looks good to me. My advice is to settle down and try it out in a sandbox state and see how myself, Madcoverboy, and others like it.

To everyone thinking of doing a rewrite: Do be advised that when I did my major rewrite of this article, I did it in a sandbox mode, and let others tweak it for a couple of weeks after I announced it. When the revised article was put into place here, everyone was happy to see it. This version will be replaced, but it is best if that happens through that same type of process as was used the last time. --EMS | Talk 14:44, 17 July 2007 (UTC)

Hi EMS! A sandbox sounds like a good idea. I guess the first consensus that needs to be reached.is how to proceed. Speaking for myself, while I will not be able to keep up my current frantic level of Wikipedia activity, I would feel comfortable gently tending to the growth of the "Consequences" and "Astrophysical applications" sections over the next few weeks in my own sandbox, re-using the current text of the "Predictions..." section and adding references as I go. It would be great if someone else could adopt the current history section, may be take some of the development history used in "Introduction to...", have another look at the history article, spend some comfortable hours with Pais or Stachel, and integrate at least in summary some things from Golden age of general relativity. Someone else could undertake to merge appropriate chunks of "Relations to other theories" with the "Overview" – I expect that, in the end, we will need to discuss the structure of the "Overview" section as well, but this would be a sensible step that can probably be taken safely before that discussion. There's work that needs to be done independently of that – find references for each alternative theory listed, convert to new citation style, that sort of thing (do we have consensus on using a separate reference list and, say, Harvnb? If I'm assuming that prematurely, please tell). I admit that's not as much fun as the other things; if no-one wants to do it (which I can understand), I'll see that I get around to it later. Once we've grown the different sections in parallel (the changes to "Overview" and "History" might need a sandbox), we'd discuss and realize that each of us would have done everything totally different, and collectively resign from WP after an acrimonious edit war reach some consensus. I would propose that only then do we tackle the lead. How does this sound? --Markus Poessel 15:15, 17 July 2007 (UTC)

I am way past being able to keep up a "frantic level" here. That is why new blood is nice. One possibiility is to set up a "WIP" (or work in progress) page under this talk page, and use that as the "sandbox". One thing that has to be decided is what to use as the base for the WIP version: My structure, Madcoverboy's, or one that you will create from scratch. Overall, I would like to use your organization, as we can alway go back to Madcoverbnoy's version from history. Onve a structure is set, and a new version drafted, I advise going through it section by section seeking consesus or at least input. I for one would hope that a new version could be up within a month or two. --EMS | Talk 15:39, 17 July 2007 (UTC)

WIP sounds like a good idea, then. Does it come with a box for the main page? As for the structure, it depends on the consensus. I like my structure, of course (should quantum gravity get its own section?); I haven't got any structure to offer for the overview (yet - for now, I would recommend the present one). One month might be a bit optimistic, two months might work. Feel free to create the WIP; I would then start merging in what I have in my sandbox so far. --Markus Poessel 17:24, 17 July 2007 (UTC)

Bringing in some parts of the overhaul

On further inspection, I found the updated "Predictions" section to be an improvement, with there being little change to my text (except for prosifying the last subsection for me) and the added illustrations. So I have moved that revised section into the current article.

I also wonder if the revised lead might be more useful that the current one, although it may still need more tweaking. Any comments on that? --EMS | Talk 15:51, 17 July 2007 (UTC)

I would recommend listening to the wisdom of opera composers. First write your opera, then compose the overture. --Markus Poessel 17:25, 17 July 2007 (UTC)

Then I will just double-check for anything else in that "overhaul" that appears to be of "high value" to me and leave the rest alone. Obviously anything I do now is subject to change during your rewrite, but where I can get a maximum of value with a minimum of effort (especially if it is due to someone else's effort) I will do so.

I recall that someone did a study of the quality of Wikipedia articles, and found that the highest quality ones were also the most editted ones. So anything of yours of Madcowboy's that can be used now is likely an asset for the article. --EMS | Talk 20:48, 17 July 2007 (UTC)

Who is madcowboy? lol Madcoverboy 01:29, 18 July 2007 (UTC)

Comments on reverted article

1. I think having an "overview" section is redundant and unspecific. I realize I had one in my revision, but that was meant as an means of introducing the equivalence principle which is semi-intuitive and comprehensible, but which is derived from more basic fundamental principals of relativity rather than being on on its own. These sections need a more rigid hierarchy and Get rid of the embedded lists !!! I would propose placing:
   1. "EFE" & "Solutions of EFE" under "Mathematics of gr"
   2. "Coordinate & Physical Acceleration" under "Justification"
   3. "Treatment of Gravitation" should be merged with the intro and whatever it displaces or is left over should be merged with "Spacetime as a curved.." since they both emphasize the role of geometry as a determinant of gravitation.

   • We don't have to call it "overview". What is meant is a section that describes the basic concepts and formulation of the theory - what Einstein published in 1916 (although explained with the hindsight of 90+ more years of research). The additional sections would then trace the consequences and new conceptual developments, the applications, the history, and alternative theories. --Markus Poessel 06:57, 18 July 2007 (UTC)

2. The "static universe" form of the EFE is duplicated in both the "EFE" section and later in the cosmology section. I believe it is more appropriate in cosmology.

   • I would still mention it when "solutions" are first introduced, but you are right in that the description itself should go into the cosmo section. --Markus Poessel 06:57, 18 July 2007 (UTC)

3. I find this statement incredibly hard to parse as an "example". It either needs an image/animation, substantial rewording, or to be removed as an "example" altogether:

   "For example: Try using a polar coordinate system in classical mechanics. In this case, an inertially moving object which passes by (instead of through) the origin point is found to first be moving mostly inwards, then to be moving tangentially with respect to the origin, and finally to be moving outwards, and yet it is moving in a straight line. This is an example of an inertially moving object undergoing a coordinate acceleration, and the way this coordinate acceleration changes as the object travels is given by the geodesic equations for the manifold and coordinate system in use."

4. My version cut out "Relationship to other physical theories" and moved it to Physical theories modified by general relativity since these modified theories are neither essential towards understanding general relativity nor entirely earthshattering/paradigm-shifting based upon my (limited) understanding of GR and multivariable calc/linear algebra. Plus the all the math looks intimidating on a top-level page. Perhaps a summary style paragraph or two on the need to modify other physical theories to reflect GR's reliance upon geometry, thus the incorporation of metric tensors.

   • As I have written before: I think the "relationships" are of different kinds and should be integrated into the other sections: mechanics probably into the basic definition, parts of electrodynamics into the "consequences", quantum mechanics would go into "Quantum gravity" or, if we want to keep it more general, "General relativity and quantum theory". --Markus Poessel 06:57, 18 July 2007 (UTC)

5. Create a "Validity" or "Generalizability" section again ("Status" seems too generic like "Overview") that merges the quantum mechanics problems mentioned in "Relationship," expands on the spacetime singularity difficulties (does any of the work with Grigori Perelman's Poincaré conjecture potentially apply here?), and addresses the alternate theories.

   • May be we could retain the idea of a "Current research and beyond" section. That would give us place for the pioneer anomaly, a place for a general remark about status and so on. --Markus Poessel 06:57, 18 July 2007 (UTC)

6. Get the John Wheeler quote back up in the body under "Spacetime as a curved..." since it is concise and illuminating. I actually don't know how I feel about the quotes section, I like the Born quote, but I imagine there are more relativity quotes out there. To me, the section seems to be begging for additional cruft to be added, which is not a good thing. Perhaps quotes might be more important/relevant in History of general relativity.

   • I seem to recall that "Quotations" sections are discouraged by some guideline or other. Wheeler should go somewhere into the main text, I suppose. --Markus Poessel 06:57, 18 July 2007 (UTC)

So say we all -- I hope! Madcoverboy 01:29, 18 July 2007 (UTC)

I think that you are making some good points and have some good ideas. Certainly in some ways you are taking this article faster and farther towards being a quality article than I could on my own even if I had the time to edit it more actively. However, we need to be careful not to throw out the baby with the bathwater: I want the improvements in style and comprehensibility, but not at the cost of technical accuracy. Unfortunately, your rewrite was a significant step back in terms of accuracy, even as it move the article forwards in other ways. Overall, any rewrite needs some time to be reviewed and to mature.

On the issues of embedded lists and the "Relationships ..." section I actually agree with you. The lists were a way of quickly categorizing the features of GR when I did my rewrite, and have been on the wane in recent months as they had become a barrier to getting GA/FA status. The "Relationships ..." section is really just a big dump of my technical knowledge on the issue and very much is too technical. However, at the time it was an improvement over what had been here before. (The loss of the "Relationships ..." section may be a good change that got lost in the revert, but please give me a day to decide on a proposal for handling this.) --EMS | Talk 05:30, 18 July 2007 (UTC)

The dispositions of the "Relationships ..." section

The "Relationships" section has been split, with the first two subsectionsbeing relegated to Physical theories modified by general relativity, and the remaining ones on the GR-QM relationship and alternate theories being made into sections in this article. The GR-QM relationsjip text has been removed from Physical theories modified by general relativity, and a link to that article added to the "Mathematics of general relativity" subsection as a "See Aslo" subheading. Hopefully that resolves this issue. --EMS | Talk 17:50, 18 July 2007 (UTC)

Great, that's a big step forward. Thanks! --Markus Poessel 19:03, 18 July 2007 (UTC)

Do we still set-up the "work in progress" sandbox, though? Or should all work be done on the main page itself? It might be OK just to do the restructuring there; some of the new sections would be a bit thin to start with, but that should soon improve... Just waiting for the word (although I'll not be able to devote more than half my wikitime to this as long as the FAC review/the re-writing for Introduction to general relativity is still going on); -- Markus Poessel 19:08, 18 July 2007 (UTC)

IMO this is a quality article and we should avoid "damaging" it as best we can. Incremental changes can and should be done in the article itself, but a major reconstruction needs to be prototyped and developed off to the side until there is a consensus in favor or letting it replace the existing article. Right now my focus is on integrating those part of the work of Madcoverboy which are a net asset into the existing article. That certainly will be an improvement, but your work may be able to take things a good bit further. WP:BOLD reads "Be bold, but don't be reckless", and IMO the only thing reckless ahout Madcoverboy's version was his replacing the existing article with it before it was properly discussed and tweaked by the community. So I call on you to set up the WIP page and start fleshing it out. Let's see what develops, and how it can best be used. --EMS | Talk 22:12, 18 July 2007 (UTC)

OK, I have created the WIP page. I have no idea how to properly advertise its existence on the main page, or on this talk page - add some kind of box at the top of the page, I suppose? I'd appreciate pointers here. --Markus Poessel 08:14, 19 July 2007 (UTC)

One thing that you need is a "WIP_talk" subpage for discussion of the WIP subpage, and a banner in the WIP version pointing people to that talk page. I strongly advise segregating the WIP talk and the (live) article talk. (Do note that improvement of the real article can and should continue even with the rewrite in progress.) --EMS | Talk 20:29, 19 July 2007 (UTC)

Only one version

Unresolved

I have noticed that at least three users (editors who use this talk page) have their own personal versions of this article (in a sandbox or other user page). And I have seen the intention expressed above to develop these separately and then substitute them for the existing version. I strenuously object to these plans. This multifurcation (Wikipedia:Content forking) will cause edit wars. It will cause wasted effort as people have to make the same changes over and over again because they were not included into someone's version which then replaced the whole article.
If you want to make a change, please make it in the one and only version, i.e. here. Pay due regard to integrating it with the recent changes made by others. Do your changes gradually, so that others can review and approve each stage before you continue to the next stage. JRSpriggs 02:52, 18 July 2007 (UTC)

I only advocated the multi-sandbox approach for parts of the article - namely: agree on the structure, parcel out the work, and then (possibly) develop the sections separately in separate sandboxes. Anyway, the currently favoured solution would be to have one "Work in Progress" page (construction site) on this talk page, and of all contributors editing there. I think that's better than editing the article directly, since the re-structuring we are about to do is likely to leave some things dangling. Either have a WOP, or we need to place a big "We apologize for the inconvenience, but there is major construction work going on". --Markus Poessel 06:48, 18 July 2007 (UTC)

My view is that this is an embarrassment of riches and needs to somehow be coordinated and managed. I agree that minor changes can and should be done on the article itself, but as I note above a major restructuring must be done off to the side. My feeling is that people can play in their sandboxes but in the end we need to either integrate the most useful parts of which version into this article or iron out the differences in a WIP (work in progress) subpage of this discussion page. (Wikipedia forwna on developmental versions being present in the article space.) --EMS | Talk 22:17, 18 July 2007 (UTC)

The template is unsightly!

The under construction template is looking huge and ugly at the top! We must remember that many of the readers who will come to the article will come only to read and not to write. They would be put off by such a huge banner advertising that this article is undergoing major work. That is a message for editors, not for readers. I suggest we place it in talk or replace it with something more discreet. Loom91 12:25, 20 July 2007 (UTC)

Thanks for insulting my very first template Loom, I will certainly change or remove it if the other editors agree.--Cronholm¹⁴⁴ 12:32, 20 July 2007 (UTC)

Come on, you can't take that personally! I'm sorry if I offended you, but in Wikipedia we are always criticising each others works. If all those were taken as personal insults the situation would become impossible. I'm merely pointing out that such a large template will distract readers and give them the impression that the article is not meant to be ready for reading yet. Loom91 13:00, 20 July 2007 (UTC)

The ALL CAPS kinda stung, but let's see what other think.--Cronholm¹⁴⁴ 13:31, 20 July 2007 (UTC)

I always advice new users of the internet to be weary of the Caps Lock. Looks like I fell victim to this old age trap, though I used Shift, not Caps Lock (is that considered a mitigating circumstance?). I apologize. Loom91 13:49, 20 July 2007 (UTC)

Anomalous perihelion precession of Mercury

The following sentence appears in the introduction: "The first success of general relativity was in explaining the anomalous perihelion precession of Mercury." Perihelion, precession and Mercury are all wikilinked but do not link to the explanation of the anomalous perihelion precession of Mercury which is described further down in the article. While the rest of the items in the introduction are clear or link to explanatory articles, this sentence requires a knowledge of the subject to be understood. Would it not be better to link "anomalous perihelion precession of Mercury" to the explanation later in the article? --CloudSurfer 08:08, 22 July 2007 (UTC)

---

And Logunov's Theory ?

Recommended change

All the banners at the top of this talk page frightened me a little bit, so I figured I'd better check in here before making a change.

In the section, "Mathematical framework", we have the following:

Local Lorentz Invariance requires that the manifolds described in GR be 4-dimensional and Lorentzian instead of Riemannian.

Then in the next section on "Geometry":

Due to the expectation that spacetime is curved, Riemannian geometry (a type of non-Euclidean geometry) must be used.

So my recommendation is to change the latter to say:

Due to the expectation that spacetime is curved, non-Euclidean geometry must be used.

Am I missing something dumb? Please tell me if I am so I don't embarrass myself.  :) VectorPosse 08:05, 15 August 2007 (UTC)

It depends on what you mean by "Riemannian geometry". Some people define it in a way that requires the signature of the metric to be all pluses and some do not. The geometry of space-time according to GTR is Riemannian in the broader sense, but not in the narrower sense. To the more picky, it is pseudo-Riemannian, i.e. Lorentzian. JRSpriggs 21:01, 15 August 2007 (UTC)

Fair enough. I don't know about physics conventions, but I agree with you that in differential geometry, a metric that isn't required to be positive definite would have to be called something other than Riemannian. In any case, this article should be edited in some manner so it doesn't appear to be contradictory (even if one interpretation is unambiguous). VectorPosse 21:21, 15 August 2007 (UTC)

Replacing "Predictions" with "Consequences..." and "Astrophysical applications"

By earlier consensus, the "Predictions" section is to be replaced by a more general section "Consequences of Einstein's Theory" (which encompasses the predictions relevant for the classical tests, but also more mathematical developments) and a section about "Astrophysical applications". I've been working on the replacement for the last few weeks, and it's now reached a stage where everything is more or less there, though in need of some polishing – I've tried to make sure that all major current GR research topics are mentioned, and that everything is properly referenced, but I haven't done much re-reading and re-editing of the resulting text. Anyway, the result can be found on the sandbox page Talk:General_relativity/WIP; I would think what's there is in a suitably advanced state to be moved to the main page right away, unless a consensus emerges that we should discuss it while it remains on the WIP page. --Markus Poessel 18:28, 30 August 2007 (UTC)

OK, since more than a week has passed without any objections, I've now moved the two sections in question, plus their references, to the main article. --Markus Poessel 08:19, 9 September 2007 (UTC)

Article length

I just briefly skimmed through Markus' edits and no one thing has jumped out at me as "wrong" or "bad" so much as how the size of the article has just exploded; 141kb is definitely too long for a WP article. That's not a bad thing, it's just too much of a good thing! :) While certainly Markus' diligent and exhaustive citations may comprise a non-trivial fraction of this length, nevertheless, some sections badly need to be cut down to summary-style length with the other content moved onto appropriate subarticles.

I am unfamiliar with the norms governing WIP pages, or the GR WIP page specifically, as I neglected to include it on my watchlist since the July conflagaration, so I'm hesitant to just dump this whole page back there again. Nevertheless, we should open the WIP page again so that we can try to edit down the sections into more digestable segments and moving the difference off into appropriate subarticles (pre-existing or new). I'd certainly be willing to give a first pass there. Madcoverboy 03:08, 10 September 2007 (UTC)

The size of the readable text is now 79 kB. As per WP:SIZE, this means "Probably should be divided (although the scope of a topic can sometimes justify the added reading time)." It hasn't run over the "magic mark" of 100 kB where splitting is compulsory. I think that, since we're dealing with a topic that is one of the cornerstones of modern physics, that is very complex (and thus, even in summary style, needs some extra space for explanation) and has quite a number of ramifications, we'd probably have a good argument that this is indeed a topic where the scope does justify the added reading time.

That said, if we can streamline the article without losing key content, we should definitely do so - with an aim of bringing it down to, say, 50 kB (which appears to be the desired length for longer articles). I've tried for summary style length in the sections I added, but there might well be further potential to streamline the text (and, as you say, probably move some things to the spin-off articles). I also think there's some potential to shorten some of the other sections. For instance, re-reading the introduction, I think the first three sections could be condensed into an overview including motivation and a summary statement of the theory itself - what's currently called "Mathematical Framework" is really mostly about the physics, as far as I can see. Also, the "Alternative Theory" section with its near-exhaustive list of alternatives could probably do with some summarizing. "Quotation" sections are discouraged, so that should probably be the first to go.

I've no idea how to best go about this and, incidentally, I'm not aware of any strict norms governing WIP pages. In earlier discussions, some have voiced concern that work on this article be kept in one place, so may be we should just work in the main article itself, or discuss selected sections here on the talk page. Since all previous versions are stored, nothing will be lost, and we can always go back and compare. Let's hear what the others, notably old hands like EMS, have to say on how to proceed from here. --Markus Poessel 07:59, 10 September 2007 (UTC)

This is never going to be a small article, but I agree that it is bloated in its current form. IMO, section 4 ("Consequences ...") is in need to some pruning. The later sections (on causal structure, horizons, singularities and evolution equations) are highly esoteric and IMO are a distraction as part of the main GR article.

I think that one thing that is needed is to determine the scope and purpose of this article. IMO, it should be a fairly technical overview of GR, mentioning the most important concepts, consequences, and areas of research for GR theory. By "fairly technical" I mean that it should be a step or two beyond Introduction to general relativity: It should directly state what the features of GR as a physicist would want them described, while at the same time trying to explain the jargon well enough so that someone who is knowledgeable about physics (but not necessarily about relativity) can get some sense of what this is all about. At the same time, my goal is for this to be an overview: Mention and breifly describe the important areas, and them move on. Although this must be more than an introduction, we still must remember that this is Wikipedia and that our audience will be more than just Ph.D.'s and graduate students. The more technical and esoteric a subtopic is, the less space it deserves, if it even deserves space here at all.

Beyond that, it is good to see some "new blood" here. As with any activity on an article, some things will improve and other things will degrade. However, the general tendency in Wikipedia is for articles to undergo an overall improvement the more that they are worked on and more importantly the more that different people work on them. --EMS | Talk 13:26, 10 September 2007 (UTC)

I agree that section 4 ("Consequences...") can probably be streamlined, but I think it would be wrong to leave out the sections you decry as esoteric. If you look at current research in relativity then, apart from the astrophysics, that is what people are working on, and if you ask a relativist for the most important results of the "Golden age", you will find that most are described in these sections. Let's summarize by all means, but let's not oversimplify the article - if the key concepts (yes, horizons, singularities, well-definedness of EFE...) aren't there, that would certainly not make for a good (let alone FA-worthy) article. --Markus Poessel 15:09, 10 September 2007 (UTC)

This is a balancing act. If it is important to the topic, then it obviously should be mentioned. The issue is how. Full sections on horizons and singularities only are going to stop most readers cold, and I mean readers who can get something out of the other sections of this article. This is not to criticise the contents of those sections: They seem to be a start to good articles of the relevant topics. They just are "too much" for this article.

My goal is for this to be a good mid-level overview of general relativity, even backing off from my own highly technical writing when appropriate. Keep in mind that there is a Wikibook on general relativity in which the whole theory can be rigirously documented, and that we can create detailed Wikipedia articles when appropriate to deal with highly technical sub-topics of general relativity. As for this article, let's find a way to describe the full scope of GR without going into mind-numbing detail on the harder-to-grasp stuff. --EMS | Talk 17:14, 10 September 2007 (UTC)

OK, I've now re-worked the Horizons section - I've given it a somewhat more appealing title, gotten rid of some of the more technical stuff (stashed away for future use in more specialized articles; some pointers remaining in footnotes), shortened some of the descriptions that are available in more detail elsewhere (notably black hole thermodynamics); all in all, this has hopefully rendered the section more accessible; it has also reduced the readable text length by a bit over 30 percent, which, if applied to the whole article, would take us from the current 79 kB text to more acceptable 54 kB. --Markus Poessel 19:43, 10 September 2007 (UTC)

That definitely helps. --EMS | Talk 01:22, 11 September 2007 (UTC)

Good – in that case, I'll gradually go over the other sections and subject them to the same treatment. --Markus Poessel 06:20, 11 September 2007 (UTC)

Singularities section now shortened by 27% as well. Hopefully also a bit more accessible now. --Markus Poessel 12:58, 11 September 2007 (UTC)

Streamlined Geodetic precession (-36%) and Gravitational lensing. (-26%) --Markus Poessel 19:47, 11 September 2007 (UTC)

You definitely have done a bunch of good work here. To be blunt about it, this article needs more work to be gotten back into a good shape, but in general the more you can slim it down and reduce the jargon the better (not that this can or should be a short jargon-free article).

I do wish to encourage you to do what you can with this article. While I have dominated this article until recently that is mostly because the Wikipedia community was satisfied with the structure that I had given it two years ago. If there is new blood and energy here, then it may be best for me to stay out of the way. Besides, I lack the time or energy to do much here for now. Just do keep in mind that making the article both informative and accessible means striking a balance between jargon and simple english, between esteric research and popular concepts, and between outright technical accuracy and brevity. There is no way to do it all here. --EMS | Talk 22:41, 11 September 2007 (UTC)

Many thanks for the encouragement! Please do not stay out of the way; I'll try to streamline the sections I added somewhat following your and Madcoverboy's remarks, but further feedback and helpful comments are of course always welcome. I'm not trying to take over the article, but I will admit to being youthfully enthusiastic about making it just so. --Markus Poessel 19:06, 12 September 2007 (UTC)

It seems to me that my interference if a few months ago, while IMO putting the article in a better place at the time, also dampenned the enthusiasm that other people had for editting it. Wikipedia articles tend to get better faster if more people work on them. I have more than had my say in the article itself, and so letting yourself and others work on it for a while may now be the best means of achieving improvement. I will certainly keep track of this article, and will at some point give it a good proofing and tweaking to deal with points that are important to me. However, for now I am willing to let others work with it and to see where it leads. In a worst case scenario I can always to a "major revert" back to an historically "good" state, but even with the issues of concern to me here I see overall improvement that itself can and should be improved upon instead of removed.

One thought for you though: This article is about due for a rewrite. I doubt that it needs anything a serious as what I did two years ago, but a fresh look at issues of article scope and structure cannot hurt. --EMS | Talk 20:35, 12 September 2007 (UTC)

OK, I'm now done with streamlining all of the new sections. Overall reduction in readable text length for those section is 35%; the total length of the article's readable text is now down to 64kB. This is still a bit too long, but I think it's now the other section's turn to be streamlined; once that done, we'll see if the desired length (around 55-60 kB or so) is reached --Markus Poessel —Preceding signed but undated comment was added at 19:46, 15 September 2007 (UTC)

I continued my streamlining program with the History section - unsuccessfully, though; the new text is only marginally shorter than the old one. Anyway, the text is now fully referenced. --Markus Poessel —Preceding signed but undated comment was added at 18:01, 19 September 2007 (UTC)

Singularities

I'm not sure what to make of one of the changes by User:JRSpriggs, namely where "the Schwarzschild solution, which describes a singularity inside an eternal static black hole (a space-like singularity shielded by a horizon)" became "the Schwarzschild solution, which describes a singularity (extended only in the time direction; but its events have a space-like separation from each other) inside an eternal static black hole (a singularity shielded by a horizon)". In what way is the Schwarzschild singularity "extended in the time direction", let alone "extended only in the time direction"? Or is that a typo? I agree the other changes (Kerr singularity) are an improvement, but I don't quite get this one. --Markus Poessel 06:26, 11 September 2007 (UTC)

That article says that the metric is

$c^{2}{d\tau }^{2}=\left(1-{\frac {r_{s}}{r}}\right)c^{2}dt^{2}-{\frac {dr^{2}}{1-{\frac {r_{s}}{r}}}}-r^{2}d\theta ^{2}-r^{2}\sin ^{2}\theta \,d\varphi ^{2}$

The singularity occurs at r = 0. Notice that as r approaches zero, a variation in the longitude or a variation in the colatitude produces a diminishing separation. Whereas variations in the time coordinate continue to give a nonzero separation (indeed it increases to infinity). However, the sign of the square is negative indicating a space like separation. JRSpriggs 01:37, 13 September 2007 (UTC)

But why "extended in the time direction"? In those coordinates (inner Schwarzschild), as far as I can see, it's extended in the t direction and the angular directions, neither of which is a time direction. --Markus Poessel 10:22, 13 September 2007 (UTC)

The t direction is the coordinate time direction. Admitedly time proceeds in the r direction within a black hole, but that does make r the time direction. So the issue is not one of correctness but rather of clarity. Perhaps including the word "coordinate" before "time" in JRSpring's text will help.

I will take a quick look at this text and see if I can do anything with it. I'm not going to promise any changes however. I personally hate the whole black hole concept and may choose to keep away from that section because of that, but if there is some obvious tweak that may clarify things a ways I will do it. Otherwise you and JRSprings need to hammer out something better (and may need to or want to even if I do an edit). --EMS | Talk 15:43, 13 September 2007 (UTC)

For the inner region, it's not even a coordinate time direction. Even a coordinate time must have a time-like tangent vector. --Markus Poessel 15:48, 13 September 2007 (UTC)

"time" or "t" is the name of the coordinate, not an attribute of it. For an external observer, that coordinate direction remains the one of time. I see your point for the internal region. However, it would cause another type of confusion if we switched coordinate names when we swtich regions. Like it or not, in GR there is no requirement that a coordinate which is semantically called the "time" direction always have a timelike tangent vector associated with it. As a practical matter, noone will call a direction the "time" direction unless that direction has a timelike tangent vector for the vast majority of the spacetime. However, inside a black hole radial space and time outright exchange roles. The makes it impossible to have a global time coordinate which also globally has a timelike tangent vector for spacetimes with black holes. (BTW - You also have trouble with the "time" coordinate in the ergosphere if a Kerr black hole. In that case, the time coordinate no longer has a timelike tangent vector, but a timelike (t,phi) vector can always be identified outside of the outer event horizon.) —Preceding unsigned comment added by Ems57fcva (talk • contribs) 17:08, 13 September 2007 (UTC)

I agree that t is a name, but to keep calling it a time coordinate is just sloppy, and a brief survey of textbooks appears to show that the writers are rather more careful about it. Misner/Thorne/Wheeler, e.g., §31.3, talk about r "chang[ing] in character from a spacelike coordinate to a timelike one" and refrain from calling t the time - on the contrary, they explicitly say that "r and t exchange roles as space and time coordinates". Likewise Ohanian/Ruffini p. 440. Rindler (Relativity) only talks about r and r coordinates. So yes, from all I can see the textbooks do seem to conform to the common usage that a "time coordinate" or "time-like coordinate" is a coordinate with a time-like tangent, as one would expect.

As for "another type of confusion", since there's a discontinuity between exterior and interior Schwarzschild, it's not a matter of simply going from one region to the other in any case – so, on the contrary, to keep calling t the time coordinate when it isn't masks what is a very real break between the interior and exterior region. If we go back to defining everything properly, then there's no problem at all – spacetime is a manifold, coordinate maps are by definition local, and it's always possible to judge whether a coordinate is a time coordinate (tangent time-like on the whole patch) or not.

In conclusion, there is a way of defining time coordinates in a consistent way; the textbooks (at least the ones I looked at) appear to be using it, and I see no reason to do things more sloppily (and to 95% or so of our intended readership more confusingly) in this article. --Markus Poessel 09:03, 14 September 2007 (UTC)

I don't have any quibble with what that text is trying to say, and I advise caution in changing it. One option is to just remove the mentions of how that Schwarzschild and Kerr singularities are extended. While I don't disagree with the text, I do find it to be awfully technical and perhaps better placed in a detailed article on the topic. (In fact, I would not mind the current sections 4.5 (Causal structure), 4.6 (horizons) and 4.7 (singularities) being exported into an article on spacetime structure in general relativity and a much breifer overview of that area presented in their place. Not only would that remove a bunch of very technical text from this article but it would also permit a more complete discussion of the relevant issues in the new ancillary article which is now dedicated to that subject area.) --EMS | Talk 15:17, 14 September 2007 (UTC)

P.S. I have now removed the text in question. The more I thought about the more I concluded that it was raising too many issues. --EMS | Talk 15:28, 14 September 2007 (UTC)

OK, I agree that it was probably more confusing that helpful to include these descriptions in the first place. In the meantime, I've done some more streamlining. The sections you mention should already be much more readable and less technical now than the original versions were; in their present streamlined and de-technicized state, they – at least in my opinion – say what needs to be said for the article to be suitably (summary-style) comprehensive. Also, I've now cut the "Evolution equation" by more than half, and, following your suggestion, started a new small article Initial value formulation (general relativity) to house the original, more technical longer version. I'll continue my streamlining spree through the added sections, and I guess after that it's time to do the same for the remaining sections. --Markus Poessel —Preceding signed but undated comment was added at 15:11, 15 September 2007 (UTC)

Discontinuity at event horizon?

To Markus Poessel: You said "... there's a discontinuity between exterior and interior Schwarzschild, ... what is a very real break between the interior and exterior region. ...". Actually, there is no discontinuity or singularity at the event horizon — it is just a typical region of spacetime. There is a problem with the Schwarzschild coordinates on that hyper-surface, but there are other coordinate systems which behave nicely there including Kruskal-Szekeres coordinates. JRSpriggs 01:31, 15 September 2007 (UTC)

Everything you say is correct. But remember that we were talking about Schwarzschild coordinates. My point was that, when writing down the metric in the usual form (as you did) and talking about exterior/interior, you're automatically talking about two different coordinate patches. As these are two different patches, it makes no sense to argue that, by continuity, t, which is a time coordinate in the exterior, should be called a time coordinate in the interior, as well. Markus Poessel 06:54, 15 September 2007 (UTC)

OK. By the way, the Schwarzschild metric is only an approximation to the metric of a physical black hole (even aside from quantum mechanical issues). There is no "white hole" in the past of a large star which explodes and leaves behind a black hole. Material falls into the black hole making it larger. And, if the universe lasts long enough, the black hole will evaporate due to Hawking radiation which means that it will eventually shrink and may not have an event horizon after all. JRSpriggs 02:07, 16 September 2007 (UTC)

Yep. In fact, I'd been thinking that a Penrose diagram for a realistic (non-eternal) black hole might make a nice illustration for either the horizon or singularity section (without the Hawking radiation bit, though). Perhaps we should explicitly mention maximally extended solutions, too. --Markus Poessel 13:41, 16 September 2007 (UTC)

Further restructuring

While I like the notion of an "advanced concepts" section, the current article structure must be a bit confusing to the reader, I think.

• The basic concept of a black hole is introduced in the "Horizons" subsection, now moved to "Advanced concepts". But this comes much later than the "Black holes" section which, together with the rest of the "Astrophysical applications", has moved up in the world (or at least in the article). Talking about black holes before the concept is even introduced is a bit awkward.
• Similarly with "Gravitational waves": one reason I put those first in the "Consequences" section was that the reader needs to know about them before he or she can understand the "orbital decay". Again, as it stands, the order is confusing - orbital decay is now described before gravitational waves have been introduced in the first place.

--Markus Poessel —Preceding signed but undated comment was added at 18:56, 20 September 2007 (UTC)

The criteria for the organization that I have chosen are first importance and then awareness and comprehensibility of the concepts. One piece of advice that I have seen in the past is to write a Wikipedia article in a way akin to how a newspaper article is written: A guick "lead" explainig what the story is, and then presenting various parts of the story ordered by anticipated interest and importance. The goal is to keep the reader engaged as long as possible. In an article like this, as long as we are providing information that is usable to the reader they will keep reading. In general, a reader will keep reading until they encounter an extended stretch of material that is over their head. So if the easier material comes first, then the readers will tend to read more of the article and get more out of it.

Obviously, the first thing to do after the lead in this article is to present the technical underpinnings of GR. Then we next get to the conseqences, which are in fact what most prople are aware of. I put time dilation and light deflection first since those are most well known and the easiest to understand. Orbital effects come next due to decreasing awareness and more difficultly comprehending what this it about. I put the detailed discussion of gravitational waves afterwards since that is the most difficult material in that section. Basically, all that someone needs to know when reading the oribital decay section is that gravitational waves are analogous to the EM waves of light. IMO we should do that and let the more long-winded explanation of gravitational waves come afterwards.

Please keep in mind that this is an encyclopedia article and not an academic text. It need to be accurate and informative. It does not need to be complete and/or technically rigorous. My goal is for a scientist who has studied GR to be able to look at it and say "this is a good write-up about GR", and for an reasonably intelligent and educated reader with limited exposure to GR to be able to read it and learn some things. So please keep the reader in mind: In the end it is the reader and not ourselves that needs to be pleased. --EMS | Talk 21:01, 20 September 2007 (UTC)

I still think it's awkward, and awkwardness rarely makes for engaging reading material. Even an encyclopedia article should follow a logical structure and introduce its concepts one by one, instead of jumping back and forth, first assuming familiarity with some concept and later explaining it as if new (the previous version wasn't completely pure in this regard, either, I will frankly admit). Ah, well, I suppose the confusion can be reduced by adding some brief definition of "black hole" when it first occurs in the main text, and ditto for "gravitational waves". --Markus Poessel 22:09, 20 September 2007 (UTC)

My concern is that taking a reader down into the bowels of GR too soon also fails to make for engaging reading material. I for one fail to see that a highly technical discussion of horizons and singularities acts as an appropriate introduction to the concept of a black hole. OTOH, they certainly should be covered in one way or another. (Black holes are an area that I am loathe to write about because I hate the concept and see it as a failing of GR. Becuase to that personal distaste for the blackhole concept, I have always felt that I cannot do it and its related subtopics justice.)

My advice is to let your mind idle a bit when looking at this article, and see how it looks. My goal is to create a tendency in this article such that the deeper you get into it the more brainpower you need to understand the discussion. I admit that you need a fair amount of brainpower to begin with here, but I don't want a Ph.D. to be a prerequisite for being able to get anything out of this article.

I do appreciate your trying to work with this structure. OTOH, if it really ends up driving you up a wall in one way on another, then feel free to change it. I am not interested in an edit war. Also, do be aware that the interplay between editors often results in the creation of a much better article than would be existed if either one had been left alone to edit as they please. So please don't treat my restructuring as an edict from "on high", but rather as a friendly and well-meaning suggestion on how this article should be structured. --EMS | Talk 13:47, 21 September 2007 (UTC)

It doesn't drive me up the wall, and I appreciate the positive effects of interplay between multiple editors. And in spite of WP:OWN, I am resolved to tread carefully when it comes to changing an article for which another has long been the main active editor. That said, I'm willing to give the new structure a try – with a quick sentence added where gravitational waves and black holes are first mentioned in the main text, it might work (grumble, grumble). --Markus Poessel 16:22, 21 September 2007 (UTC)

An adjustment to the restructuring

I have concluded that my putting the gravitational waves section after the orbital decay subsection is causing more trouble than that ordering is worth. So I have moved the gravitational waves section up to be above the orbital effects section. (I figured that I had to be the one to do this since Marcus wants to respect my decisions regarding this article.) --EMS | Talk 04:36, 23 September 2007 (UTC)

OK, that looks like a good compromise. --Markus Poessel 06:44, 23 September 2007 (UTC)