Wikipedia:Featured article candidates/General relativity

The following is an archived discussion of a featured article nomination. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.

The article was promoted by User:SandyGeorgia 04:29, 27 June 2008 [1].

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General relativity

previous FAC

Self-nominator I've been re-working this article since July 2007 and, after the recent helpful peer review, I am confident it now meets all the FA criteria. Main contributors: When I came aboard in 2007 and started streamlining the text and adding quotations, EMS had already done a substantial amount of work. Since then, there have also been numerous additions and improvements by MP and JRSpriggs. Markus Poessel (talk) 02:00, 19 June 2008 (UTC)

Comments

• http://einstein.stanford.edu/content/exec_summary/GP-B_ExecSum-scrn.pdf current ref Everitt C. W. F., Parkingosn, Bradford & Kahn is lacking a publisher
• I see http://www.astro.ucla.edu/~wright/cosmolog.htm is hosted by UCLA, what makes the author important? I'm assuming he's a professor? It's also missing a publisher

Otherwise sources look good, the links all checked out with the link checker tool. Ealdgyth - Talk 13:06, 19 June 2008 (UTC)

Thanks for your additional comments!

• Everitt et al.: Have added "Project Report: NASA, Stanford University, Lockheed Martin"
• Wright: I'd gone ahead and added a link to the author's Wikipedia entry, Edward L. Wright, when I noticed that I'm not citing that reference anywhere. Must have missed it on my removing-uncited-references run; have removed it now.

Glad to hear everything else checks out. Markus Poessel (talk) 13:32, 19 June 2008 (UTC)

Support As they did with Introduction to general relativity, Markus and the other GR editors have made a thoughtful and accessible and ESSENTIAL encyclopedia article worthy of featured status. Madcoverboy (talk) 14:52, 19 June 2008 (UTC)

Support - overall seems very good. I have a few quibbles, mostly about prose, though:

Resolved comments from Nousernamesleft^{copper, not wood}

• Both British and English spelling are present in the article: i.e. "modelling" as well as "generalization" and others. It seems predominantly British, so I advise changing the American spellings.

Note that -ize spelling is gaining ground in UK english. I believe the Oxford for example actually has "generalization" as the dominant spelling now. So, I think this might not be a very big issue. (TimothyRias (talk) 08:59, 20 June 2008 (UTC))

I don't think this is correct: since the 1970s, there has been a significant move from the zed to the es. The OED is widely deprecated for failing to adjust the order of its spellings (still zed first—unbelievable). TONY (talk) 11:40, 21 June 2008 (UTC)

The main is though that using -ize with UK spelling is not necessarily incorrect. I suggest sticking with -ize since (among other things) it is the preferred spelling for journals like Nature. The use should be consistent throughout the article though. (TimothyRias (talk) 08:35, 23 June 2008 (UTC))

According to WP:SPELLING the -ize is acceptable. Awadewit (talk) 11:16, 23 June 2008 (UTC)

I'm glad to hear that -ize is acceptable. The current use is consistent, as I just re-checked. Markus Poessel (talk) 12:58, 23 June 2008 (UTC)

• "From classical mechanics to general relativity" sounds... awkward. Couldn't it be changed to something like "Origins in classical mechanics"?
• "1915/16"? Does it mean that a single work was published in multiple volumes, or that multiple works were published? If it's the latter, then it should probably be "1915–16".
• "Examples are gravitational time dilation, the gravitational redshift of light, and the gravitational time delay; the theory's predictions have been confirmed in numerous observations and experiments." - seems to changed subject in the middle of the sentence.
• "Still, a number of open questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity." - is the "open" really necessary? The context implies they're not solved, and therefore open.

I think the use of "open" in this context is fine. Yes, it is implied by the context. But, it very customary to talk about "open" problems/questions when talking about a field of research. Being explicit helps readers that briefly skimming the text. (TimothyRias (talk) 08:59, 20 June 2008 (UTC))

• "There is evidence that, indeed, such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects (such as active galactic nuclei or microquasars)" - why are the parentheses necessary?
• Redundancy: "Nevertheless, a number of exact solutions are known, although only a few of them have direct physical applications."
• More redundancy: "There are some exact solutions describing gravitational waves, for instance a wave train traveling through empty space"

Nousernamesleft^{copper, not wood} 03:17, 20 June 2008 (UTC)

I just drive-by-fixed the parenthetical bit before signing off for the night. I might comb through the article later. I'm not a regular editor of the article. {{Nihiltres

Replies by Markus Poessel to the preceding comments by Nousernamesleft^{copper, not wood}

• British vs. American spelling: is there, by any chance, a helpful tool that ferrets these spelling variants out?
• "From classical mechanics to general relativity" vs. "Origins in classical mechanics" - your suggested replacement doesn't quite hit the mark. The section itself is a progression from classical mechanics to an unusual interpretation of Newtonian gravity to the inclusion of special relativity to general relativity. I wouldn't want to overstress "classical mechanics". I tried to come up with another title during the review (as, per the MOS, any section title that has the article title in it needs special scrutiny), but couldn't come up with a suitable alternative.
• "1915/16" - the work was presented at a session of the Prussian Academy of Sciences in late 1915, and the proceedings of that session were published in early 1916. Should we be more explicit? Or say "presented" in 1915?
• "Examples are gravitational time dilation,...": changed second part to "the theory's predictions regarding these effects have been confirmed in ...".
• "open questions" - I would agree with TimothyRias that it is a common expression. And in writing about research, it is not uncommon to ask questions and then answer them for the reader (although that's not my particular writing style), so yes, the openness of a question is worth pointing out, I think.
• Quasars/Microquasars: you're right, and I see you have already removed the parantheses.
• "a number of exact solutions" - I would like to leave that in there. Many people are used to an equation having only one or a few solutions. Here, we have a huge potential of possible solution, know a considerable number (but negligibly small with what we could know), and only a few of them are relevant for astrophysics.
• "some solutions for gravitational waves" - removed "some".

Thanks for your support, and your comments! Markus Poessel (talk) 17:33, 20 June 2008 (UTC)

I've fixed the 1915/16 phrasing to "presented by Albert Einstein in 1915 and published the following year". Is the result satisfactory? It still seems slightly awkward, to me, in that the detail of its being presented one date and published another is tangential to the definition of the topic, but the date issue is now explicit. {{Nihiltres|talk|log}} 23:28, 20 June 2008 (UTC)

• Comment Use en dashes for page ranges, chapter ranges, etc. in references and all over the article, per WP:DASH. Gary King (talk) 04:24, 20 June 2008 (UTC)

• Brighterorange has a wonderful bot that can fix these dash issues. If you ask him nicely, he'll run it on the article for you! Awadewit (talk) 20:25, 20 June 2008 (UTC)

• Thanks for the hint Awadewit, but I read it only after going through the article by hand. The five (out of 150 or so) cases that escaped earlier scrutiny have been fixed now. Markus Poessel (talk) 20:35, 20 June 2008 (UTC)

Comment The part that I've read up to now (until Definitions and basic applications) is very well written, so if the article continues like that I will support. Some comments on the contents:

• The lead section does not explicitly mention that general relativity is currently accepted as the working theory of gravity by most. Why? I'd guess that's one of the most important things about general relativity (presuming it's true).
• I had to read the sentence "When, in 1929, the work of Hubble and others made it clear that our universe is indeed expanding, and thus better described by expanding cosmological solutions found by Friedmann in 1922, Lemaître formulated the earliest version of the big bang models." in the history section a couple of times. Perhaps it can be rewritten?
• I stumbled upon "Space, in this construction, still has the ordinary Euclidean geometry." in Geometry of Newtonian gravity. It took me a while to realize that you probably mean that space is Euclidean, but spacetime is not. That is, if you restrict the connection to the three spatial dimension, you get the connection of non-curved Euclidean space (I forgot what this connection is called). Correct?

-- Jitse Niesen (talk) 10:03, 20 June 2008 (UTC)

• Lead section: talk about missing the obvious... I've fixed it now. Good catch.
• Hubble: that is a consequence of the times when the article was much longer than it is now, and underwent massive streamlining. Streamlining seems to have gone too far, here, as your comment indicates. I've expanded that passage.
• Euclidean space: you read the sentence correctly. I've expanded the description a bit to, hopefully, make it clearer.

Thanks for your comments! Markus Poessel (talk) 20:50, 20 June 2008 (UTC)

Copy-edit throughout would be great. It's not badly written, but needs a few rough edges shaved off by someone who's unfamiliar with the text. Even a non-expert. Here are quite random examples.

• "Still, a number of open questions remain,"—Replace "still" with "however".
• Can you dispense with "indeed" in this formal register?
• "classical mechanics and Newton's law of gravity admit of a geometric description"—ungrammatical. And MOS doesn't like "one" much (see following sentence).
• It's highly technical (see the opening), and it's full of valuable links. Why, then, are such simple items as "lines" and "speed" linked? I'd ration them throughout.
• "In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics." Should that colon be a comma?
• "They are defined by the set of light cones (see the image on the left). The light-cones define a causal structure: for each event A,...". I never like "see ...". Why not: "They are defined by the set of light cones. In the image, the light-cones define a causal structure: for each event A,...". TONY (talk) 11:40, 21 June 2008 (UTC)

I'm concerned to hear that, in previous copy-editing runs, we missed some of the passages that should have been corrected. I've made about half of the concrete changes you suggest; the reasons I did not make the others are as follows:

• There is one remaining "indeed" (in a footnote) that seems to be necessary.
• In what way is "classical mechanics and Newton's law of gravity admit of a geometric description" ungrammatical?
• "In the language of symmetry: where gravity can be neglected," - replacing that colon with a comma is not an option. It would imply that, when we use the language of symmetry, that means that gravity can be neglected. Instead, what follows after the colon is a description in the language of symmetry.
• Light-cones: I could change "see" to "cf." or similar, but your reformulation would change the meaning. That the light-cones define a causal structure is true in general, not only in the image.

Many thanks for your comments. Markus Poessel (talk) 14:26, 22 June 2008 (UTC)

Update: some users, notably WillowW and MP, have now kindly started another copy-editing run, and are hopefully shaving off whatever rough edges you were concerned with. Markus Poessel (talk) 17:36, 23 June 2008 (UTC)

Support - with a few comments.

• The first sentence as become untidy with recent edits wrt the presentation year and publication years.
• This sentence It unifies special relativity and Newton's law of universal gravitation, resulting in a description of gravity as a property of the geometry of space and time.' Would be better if resulting in a description simply read and describes.
• There's tautology in open questions remain, how about simply there are unanswered questions?
• The novel effects are not novel in the sense of new, here it should be 'newly discovered.
• Why the use of curious wrt gravitational lenses? One of the many delights of relativity is that this phenomenon was predicted and is fully explained.
• The introductory paragraph of Definition and basic applications:

The derivation outlined in the previous section contains all the information needed to define and characterize general relativity. Having defined the theory, we will enumerate some of its properties and then address a question of crucial importance in physics: how the theory can be used for model-building.

Should be depersonalised. I don't like the non-encyclopedic, lecture-like, we....

Last, it would have been nice to have read that Einstein later considered the invention of the cosmological constant as the biggest mistake of his life. Thanks for a superb article, one that forms the core of all great encyclopedias, you should be very proud. GrahamColm^Talk 16:17, 21 June 2008 (UTC)

Thanks for your comments and your support. I have made changes that (hopefully) address all of your concerns. Markus Poessel (talk) 18:27, 21 June 2008 (UTC)

Comment (following up from above):

• In the section Definition and basic properties: "Instead, gravity changes the properties of space and time, which changes the straightest-possible paths that objects will naturally follow. The curvature is, in turn, caused by the energy-momentum of matter." The first sentence says that gravity causes curvature, the second says that energy-momentum causes curvature. Huh?
• In the Horizons section, it says: "by the second law of black hole mechanics, the area of the event horizon of a general black hole will never decrease with time." But then it talks about Hawking radiation, which does cause black holes to shrink; that seems to contradict each other. I assume that the radiation carries an entropy increase that compensates for the entropy decrease caused by the shrinking black hole, but this is way beyond my knowledge, so I'd prefer for someone else to fix it.
• The penultimate sentence ends with "in the hope of creating opportunities to test the theory beyond the limited approximations it has been tested so far even in the binary pulsar measurements." That seems rather convoluted, perhaps even grammatically incorrect; I can't figure out the sentence construction.

Thanks for addressing my earlier comments. -- Jitse Niesen (talk) 16:22, 23 June 2008 (UTC)

All good points – I have made changes that, I hope, will address your concerns. Thanks for your additional comments! Markus Poessel (talk) 19:02, 23 June 2008 (UTC)

Support A very good article, comprehensive, with many references. There are some sentences that appear too long, with too many commas. Perhaps these can be shortened; I have made some attempt to do this for part of the article. I also have a gripe about there being too many statements of the form A : B. For example, In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics. I think the colon could be replaced by a comma for better flow. If these can be cleared up (not necessarily all of them), and the prose improved slightly, then that should improve the article. MP ^{(talk•contribs)} 17:57, 23 June 2008 (UTC)

Thanks for your support, and your comments – and, incidentally, for your previous edits. If you have any specific long or colon-infested sentences to get rid of, I'm open to suggestions. Your concrete example, though, is one where the change from colon to comma would greatly encourage a misunderstanding (as I mentioned in my reply to TONY, above), so I would like to keep that. Markus Poessel (talk) 19:09, 23 June 2008 (UTC)

A note for future reference. There is excess markup (bolding) throughout this section and unsigned "Resolved" and "done" comments; since the reviewer has indicated Support, I'm not going to take the time to step back through the page diffs to find out who marked the items done and resolved, but on future FACs, please sign your entries. SandyGeorgia (Talk) 17:20, 26 June 2008 (UTC)

Coincidentally, I've just asked a number of people if they could hide their resolved comments in cap box templates. That should make the discussion a bit more readable, I hope. Markus Poessel (talk) 18:28, 26 June 2008 (UTC)

Hi and thanks. Firstly, let me just say that you have transformed the article (virtually single-handedly) into a superb one since EMS' revision. Excellent work. I have not made significant changes to this article in a long while, but when I saw the FAC discussion, it motivated me to help out. I've just finished going through the article and performed any changes I could immediately make. Let's deal with the colons and semicolons first. My general concern re colons and semicolons in this article is that there are too many of them; I believe this makes the article flow less smoothly. The following may be long-winded and obsessive, but I will list here all the colon phrases/sentences in the article. Then, perhaps underneath each 'suspect', we can discuss if a change is required. I'll probably start the discussion with a complaint and an alternative, but we can take it from there.

In Geometry of Newtonian gravity:

• The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed.
  • This is probably ok, so I suggest keep.
    • Agreed. Markus Poessel (talk) 20:58, 23 June 2008 (UTC)
      • Resolved.

• According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors, there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.[15]
  • Take out the colon and replace with , where the trajectory of a test body...
    • One nice thing about colons is that they provide a bit of a break, exactly because they break the flow. Here, my hope was that the colon would allow the reader to breathe before going on to the second part of the statement. Markus Poessel (talk) 20:58, 23 June 2008 (UTC)
      • Ok, I agree. Keep. MP ^{(talk•contribs)} 16:13, 25 June 2008 (UTC)
        • Resolved.

• A simplified version of this is embodied in Einstein's elevator experiment, illustrated in the figure on the right: for an observer in a small enclosed room, it is impossible to decide, by mapping the trajectory of bodies such as a dropped ball, whether the room is at rest in a gravitational field, or in free space aboard an accelerated rocket.[16]
  • Replace colon with full stop and start a new sentence with For an observer...
    • Mm. I think the colon makes it more readable – it shows that the two sentences are connected, and in fact the second one directly describes the outcome of the experiment. Since the second sentence doesn't repeat the word "elevator", that connection might not be a bad thing... Markus Poessel (talk) 20:58, 23 June 2008 (UTC)
      • Fair enough. Keep it. MP ^{(talk•contribs)} 16:13, 25 June 2008 (UTC)
        • Resolved.

• As can be shown using simple thought experiments following the free-fall trajectories of different test particles, the result of transporting spacetime vectors that can denote a particle's velocity (time-like vectors) will vary with the particle's trajectory; in mathematical terms: the Newtonian connection is not integrable.
  • Ouch - the semicolon and colon ! After the semicolon, write mathematically, the Newtonian connection is not integrable.
    • I could agree to "mathematically speaking"; just "mathematically" sounds as if there were a mathematical and non-mathematical way of being integrable that could readily be assumed to apply in this situation. Markus Poessel (talk) 20:58, 23 June 2008 (UTC)
      • I can make that compromise. I'll fix it. MP ^{(talk•contribs)} 16:54, 24 June 2008 (UTC)
        • Done.

• The result is a geometric formulation of Newtonian gravity using only covariant concepts, in other words: a description which is valid in any desired coordinate system.[17]
  • Replace with The result is a geometric formulation of Newtonian gravity using only covariant concepts, i.e. a description which is valid in any desired coordinate system.[17]
    • Agreed: changed. Markus Poessel (talk) 14:37, 24 June 2008 (UTC)
      • Done.

In Relativistic generalization:

• In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics. (The defining symmetry of special relativity is the Poincaré group which also includes translations and rotations.)
  • As Markus explained above a few times, this should be kept: keep.
    • Resolved.

• The light-cones define a causal structure: for each event A, there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light (such as event B in the image), and a set of events for which such an influence is impossible (such as event C in the image).
  • Take out the colon and replace with a full stop and start a new sentence with For each event A,...
    • Again, isn't that the function of a colon: to make clear that what follows is more closely connected to the preceding sentence than a full stop would indicate? I usually read these texts aloud to myself to get a proper feeling for how they flow. When I read with a full stop here, I do come to a stop. With a colon, there is a caesura, but it is clear that there is no real break. So no, I would vote to keep the colon here. I'm convinced this is one of the things colons were made for: the "special function... of delivering the goods that have been invoiced in the preceding words" (Fowler, who doesn't like colons that much) Markus Poessel (talk) 14:37, 24 June 2008 (UTC)

• But the light-cones, in conjunction with the world-lines of freely falling particles, contain even more information: they can be used to reconstruct the space-time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure.[22]
  • No need to say there's more info. It's implied once the above is replaced with, In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the space-time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure.[22]
    • Agreed. Changed. Markus Poessel (talk) 14:37, 24 June 2008 (UTC)
      • Done.

• Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames.
  • Probably keep this one ?
    • I'd say so. Markus Poessel (talk) 14:37, 24 June 2008 (UTC)
      • Resolved.

• Instead there are approximate inertial frames moving alongside freely falling particles. Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.[23]
  • Replace with, Instead, there are approximate inertial frames moving alongside freely falling particles. In the spacetime setting, the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.[23]
    • I don't think that's quite the same meaning. I wanted to make the point that there are different languages one can use to describe this, one of them being that of spacetime geometry. Markus Poessel (talk) 20:19, 24 June 2008 (UTC)
      • Ok. MP ^{(talk•contribs)} 16:13, 25 June 2008 (UTC)
        • Resolved.

In Einstein's equations:

• Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely.
  • Probably keep
    • Agreed. Markus Poessel (talk) 20:19, 24 June 2008 (UTC)
      • Resolved.

In Definition and basic applications:

• The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics: how the theory can be used for model-building.
  • Replace with, The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely, how the theory can be used for model-building.
    • Agreed, changed (w/o the comma after the "namely", though). Markus Poessel (talk) 20:19, 24 June 2008 (UTC)
      • Done.

In Definition and basic properties:

• Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories), correspond to inertial motion within a curved geometry of spacetime in general relativity: there is no gravitational force deflecting objects from their natural, straight paths.
  • Replace the colon with a semicolon ?
    • I agree that is an improvement. Changed. Markus Poessel (talk) 20:19, 24 June 2008 (UTC)
      • Done.

• As it is constructed using tensors, general relativity exhibits general covariance: its laws—and further laws formulated within the general relativistic framework—take on the same form in all coordinate systems.[35]
  • Probably keep.
    • I would agree. The sentence after the colon explains what the sentence before only mentions: general covariance. Markus Poessel (talk) 20:26, 24 June 2008 (UTC)
      • Resolved.

In Light deflection and gravitational time delay:

• Closely related to light deflection is the gravitational time delay (or Shapiro effect): light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction.[62]
  • Replace with, Closely related to light deflection is the gravitational time delay (Shapiro effect), where light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction.[62]
    • I'm not sure the "where" works. "due to which" would be closer to the mark, but seems awkward. Again, since this is what a colon is meant to do, I would like to keep it. Markus Poessel (talk) 20:26, 24 June 2008 (UTC)
      • How about, Closely related to light deflection is gravitational time delay (Shapiro effect), the phenomena whereby light signals take longer to move through a gravitational field than in the field's absence. There have been numerous successful tests of this prediction.[62] MP ^{(talk•contribs)} 16:24, 25 June 2008 (UTC)
        • OK, implemented with small changes. Markus Poessel (talk) 19:13, 25 June 2008 (UTC)

In Gravitational waves:

• One of several analogies between weak-field gravity and electromagnetism is that, analogous to electromagnetic waves, there are gravitational waves: spacetime ripples which propagate at the speed of light.[64]
  • • Again, what follows the colon explains "gravitational waves" – this is, I think, the quickest way to do so. Markus Poessel (talk) 20:26, 24 June 2008 (UTC)

In Orbital decay:

• Not so for a close binary pulsar, a system of two orbiting neutron stars, one of which is a pulsar: from the pulsar, observers on Earth receive a regular series of radio pulses that can serve as a highly accurate clock, which allows precise measurements of the orbital period.
  • This is less clear to me than the others, but I would still vote "keep". A full stop would leave the sentence "Not so" without a clear connection to what the "Not so" means. Markus Poessel (talk) 20:26, 24 June 2008 (UTC)

In Geodetic precession and frame-dragging:

• One is geodetic precession: the axis direction of a gyroscope in free fall in curved spacetime will change when compared, for instance, with the direction of light received from distant stars—even though such a gyroscope represents the way of keeping a direction as stable as possible ("parallel transport").[81]
  • Again: what comes after the colon directly defines what comes before. It could also be "geodetic precession, the fact that the axis direction", but I think that is less elegant. Markus Poessel (talk) 20:26, 24 June 2008 (UTC)

In Black holes and other compact objects:

• Whenever an object becomes sufficiently compact, general relativity predicts the formation of a black hole: a region of space from which nothing, not even light, can escape.
  • Replace with, General relativity predicts that a sufficiently compact object will form a black hole, a region of space from which nothing (even light) can escape.
    • That works for me. Changed. Markus Poessel (talk) 20:26, 24 June 2008 (UTC)
      • Done.

• Black holes are also sought-after targets in the search for gravitational waves (cf. Gravitational waves, above): merging black hole binaries should lead to some of the strongest gravitational wave signals reaching detectors here on Earth, and the phase directly before the merger ("chirp") could be used as a "standard candle" to deduce the distance to the merger events–and hence serve as a probe of cosmic expansion at large distances.[108]
  • OK – I don't think the first sentence is so dependent on the second as to make the colon important, so it works with a full stop instead. Changed. Markus Poessel (talk) 20:49, 24 June 2008 (UTC)
    • Done.

In Cosmology:

• Once a small number of parameters (for example the universe's mean matter density) have been fixed by astronomical observation,[113] further observational data can be used to put the models to the test:[114] successful predictions include the initial abundance of chemical elements formed in a period of primordial nucleosynthesis,[115] the large-scale structure of the universe,[116] and the existence and properties of a "thermal echo" from the early cosmos, the cosmic background radiation.[117]

• • That works both ways, I guess. Changed. Markus Poessel (talk) 00:04, 25 June 2008 (UTC)
    • Done.

In Horizons:

• The best-known examples are black holes: if mass is compressed into a sufficiently compact region of space (as specified in the hoop conjecture, the relevant length scale is the Schwarzschild radius[129]), no light from inside can escape to the outside.

• • I think that, here, the colon is the most efficient way of linking the sentences. With a comma, the sentence would run to too many clauses. With a full stop, "black hole" would need to be repeated. Markus Poessel (talk) 00:04, 25 June 2008 (UTC)

• Using global geometry, later studies have revealed more general properties of black holes: in the long run, they are rather simple objects characterized by eleven parameters specifying energy, linear momentum, angular momentum, location at a specified time and electric charge.
  • Replace the colon with a full stop and start a new sentence with In the long run,...'
    • Works for me. Changed. Markus Poessel (talk) 15:21, 25 June 2008 (UTC)
      • Done.

• This is stated by the black hole uniqueness theorems: "black holes have no hair", that is, no distinguishing marks like the hairstyles of humans.
  • Probably keep.
    • Agreed. Connection is sufficiently close. Markus Poessel (talk) 15:32, 25 June 2008 (UTC)
      • Resolved.

• There are other types of horizons: in an expanding universe, an observer may find that some regions of the past cannot be observed ("particle horizon"), and some regions of the future cannot be influenced (event horizon).[135]
  • Since this is at the beginning of a paragraph, full stop should work. Changed. Markus Poessel (talk) 15:32, 25 June 2008 (UTC)
    • Done.

In Singularities:

• The famous singularity theorems, proved using the methods of global geometry, say otherwise: singularities are a generic feature of general relativity, and unavoidable once the collapse of an object with realistic matter properties has proceeded beyond a certain stage[141] and also at the beginning of a wide class of expanding universes.[142]
  • Since the second part delivers what the first part promises, I'd like to keep the colon. Especially since it fits in so naturally with the verb "say". Markus Poessel (talk) 15:42, 25 June 2008 (UTC)
    • Ok. MP ^{(talk•contribs)} 16:13, 25 June 2008 (UTC)
      • Resolved.

In Evolution equations:

• Each solution of Einstein's equation encompasses the whole history of a universe—it is not just some snapshot of how things are, but a whole spacetime: a statement encompassing the state of matter and geometry everywhere and at every moment in that particular universe.
  • On re-reading, I didn't quite like that sentence. I've reformulated this, which also got rid of the colon. Markus Poessel (talk) 15:42, 25 June 2008 (UTC)
    • Done.

• By this token, Einstein's theory appears to be different from most other physical theories, which specify evolution equations for physical systems: if the system is in a given state at some given moment, the laws of physics allow extrapolation into the past or future.
  • I'd like to keep that one. Second part directly explains what is meant by the first part. Markus Poessel (talk) 15:42, 25 June 2008 (UTC)
    • Fair enough. MP ^{(talk•contribs)} 16:13, 25 June 2008 (UTC)
      • Resolved.

• These decompositions show that the spacetime evolution equations of general relativity are well-behaved: solutions always exist, and are uniquely defined, once suitable initial conditions have been specified.[147]
  • Keep, for the same reasons as the previous one. Markus Poessel (talk) 15:42, 25 June 2008 (UTC)
    • Agreed. MP ^{(talk•contribs)} 16:13, 25 June 2008 (UTC)
      • Resolved.

In Quantum gravity:

• The demand for consistency between a quantum description of matter and a geometric description of spacetime,[161] as well as the appearance of singularities (where curvature length scales become microscopic), indicate the need for a full theory of quantum gravity: for an adequate description of the interior of black holes, and of the very early universe, a theory is required in which gravity and the associated geometry of spacetime are described in the language of quantum physics.[162]
  • Keep, for the same reasons. Second part describes what that need is. Markus Poessel (talk) 15:42, 25 June 2008 (UTC)
    • Agreed. MP ^{(talk•contribs)} 16:13, 25 June 2008 (UTC)
      • Resolved.

• One attempt to overcome these limitations is to formulate a quantum theory not of point particles, but of minute one-dimensional extended objects: string theory.[166]
  • Replace with, One attempt to overcome these limitations is string theory, a quantum theory not of point particles, but of minute one-dimensional extended objects called strings.[166]
    • Works for me. Changed. Markus Poessel (talk) 15:42, 25 June 2008 (UTC)
      • Done.

• Using the initial-value-formulation of general relativity (cf. the section on evolution equations, above), the result is an analogue of the Schrödinger equation: the Wheeler-deWitt equation which, regrettably, turns out to be ill-defined.[171]
  • Replace with, Using the initial-value-formulation of general relativity (cf. the section on evolution equations, above), the result is the Wheeler-deWitt equation (an analogue of the Schrödinger equation) which, regrettably, turns out to be ill-defined.[171]
    • OK. Changed. Markus Poessel (talk) 15:42, 25 June 2008 (UTC)
      • Done.

MP ^{(talk•contribs)} 20:11, 23 June 2008 (UTC)

• Support, but I have a few comments:

1) The article writes Einstein equations as

$G_{ab}=\kappa \,T_{ab},$

One unexplained tensor is proportional to another. As written the equations are pretty useless for a reader not familiar with the GR. I suggest writting something more informative, like this at least

$R_{ab}-{\textstyle 1 \over 2}R\,g_{ab}=-{8\pi G \over c^{4}}T_{ab},\quad R_{ab}={R^{k}}_{akb}\quad R={R^{k}}_{k},$

where G (and other parameters are) is ...

2) It would be desirable to mention that the equations in empty space-time are simply

$R_{ab}=0$

3) The article contains only one formula. However writing expression for the gravitational radius may be beneficial for 'Black holes and other compact objects' subsection.

4) It should be stressed that the motion of matter in GR can not be arbitrary chosen—the (covariant) divergence of energy-momentum tensor must be zero. So the GR imposes the strong conditions on the laws that govern the matter. This is a big difference with Maxwell equations that require only charge conservation.

Ruslik (talk) 08:42, 25 June 2008 (UTC)

• 1) and 2): I agree that the formula using Ricci tensor and scalar is of better use to those who are not skipping the formulae anyway. I've reformulated that section, and added the vacuum equations.
• 3) I don't think it fits in the astrophysics section very well. We did have it in the "Horizons" section, where the Schwarzschild radius is mentioned explicitly. It got axed when streamlining was the order of the day, but I'll be more than happy to put it back.
• 4) A very good point. I've made a change that should take care of it.

Thanks for your comments and your support! Markus Poessel (talk) 15:20, 25 June 2008 (UTC)

• Support, with warm congratulations to Markus on so successful an article. I left some minor points on the Talk page, but I'm sure that those will be resolved to everyone's satisfaction. Willow (talk) 21:59, 25 June 2008 (UTC)

Comment – this is pure nitpicking, but some wikilinks point to disambiguation pages. I've fixed some and tagged a number of others. In such a highly technical article, accurate links are important. {{Nihiltres|talk|log}} 04:05, 26 June 2008 (UTC)

Thanks for your comment, and for fixing misleading wikilinks. I've just gone through the whole article once more, catching some links that didn't quite lead where they were meant to lead, but which had escaped earlier sweeps. Markus Poessel (talk) 18:10, 26 June 2008 (UTC)

The above discussion is preserved as an archive. Please do not modify it. No further edits should be made to this page.