Talk:Anti-de Sitter space

Introduction for non-expert
I substituted saddle and trumpet bell as examples of surfaces with hyperbolic or negative curvature. A bowl, being spherical, is not such a good example because it has positive curvature whether viewed from the inside or outside. Similarly in the following section on the rubber-sheet analogy I pointed out the trumpet-bell-shaped (rather than bowl-shaped) nature of the depression, responsible for the inward deviation of trajectories passing nearby.CharlesHBennett (talk) 05:04, 8 May 2010 (UTC)

Strictly speaking, the claim that ″Energy and matter are equivalent″ is incorrect, and should be changed to ″Energy and mass are equivalent″. ′Matter′ is another matter entirely! :-) George963 au (talk) 00:21, 6 April 2018 (UTC)

Article needs much work
This article should probably be split: Both revised articles should begin with much simpler intros for laypersons, and should have better citations. The second should have citations in WikiProject GTR format.---CH (talk) 01:54, 15 September 2005 (UTC)
 * 1) n-dimensional AdS, with better explanation of important work in math and non-gtr theories, with some interesting general coordinate charts such as Hopf charts,
 * 2) the four dimensional example, with discussion of nice coordinate charts as in Hawking and Ellis

half-space chart
Is it the y coordinate which is bounded from one side? --MarSch 17:43, 1 November 2005 (UTC)


 * Hi, MarSch, in the given chart $$y > 0 $$, as for upper half space model of Hn. Yes, anyone typing in a line element should always repeat  always  add the intended ranges of the coordinates.  Few simple actions can be as helpful in avoiding potential confusion in this subject!---CH 20:06, 5 February 2006 (UTC)

Geodesic boundary
The geodesic boundary, i.e. "the limit as y goes to 0", should be explained in some detail.

Blank image
The "picture" on the page is completely blank. It presumably should be removed or replaced. Gene Ward Smith 21:52, 4 May 2006 (UTC)
 * Picture works OK for me. A red cylinder sliced at two green ellipses.  Maybe it's your browser?  You might consider switching to a more PNG friendly browser if you haven't already.  PNG has been a W3C standard for a decade and it's the recommended format on Wikipedia, after all. -lethe talk [ +] 22:05, 4 May 2006 (UTC)

Best definition of AdS space?
In the current definition anti de Sitter space is defined as a space which is simply connected. But this is not in agreement with the definition in e.g. [].

The best (?) definition of anti de Sitter space of dimension n+1 should be the solution to the equation
 * $$x_1^2 + x_2^2 + x_n^2 - x_{n+1}^2 - x_{n+2}^2 = -1, $$

that is, the same as,
 * $$x_1^2 + x_2^2 + x_n^2 + 1 = x_{n+1}^2 + x_{n+2}^2 $$;

that is, as a one-sheeted hyperboloid in $$R^{n+2}$$. — Preceding unsigned comment added by Ulner (talk • contribs) 23:59, 5 May 2006

This article managed to entirely confuse me, until I came to the talk page and saw the above comment, which concisely says it all. In the main article ADS is defined more generally and at no point is it spelled out how or when it specialises to this. The notation simply switches inexplicably between sections. — Preceding unsigned comment added by 2A01:56C0:8180:0:3C75:FB77:779F:3D4 (talk) 19:26, 7 November 2016 (UTC)

Exactly. I'm writing from a relativity conference at the ESI Institute, in Vienna. The talk being given is on anti-de Sitter space, and this article is confusing even to a so-called expert !!

Let me slightly edit the above definition. The quickest definition of anti-de Sitter space of dimension n+1 should be as the solution to the equation
 * $$x_1^2 + x_2^2 + \cdots + x_n^2 - x_{n+1}^2 - x_{n+2}^2 = -1, $$

which is a one-sheeted hyperboloid in $$R^{n+2}.$$ It has the topology of $$R^n\times S^1.$$ It becomes a Lorentz manifold, with the $$S^1$$ timelike, by restricting to it the ambient metric $$g$$ of signature (n,2) given by
 * $$g = dx_1^2 + dx_2^2 + \cdots + dx_n^2 - dx_{n+1}^2 - dx_{n+2}^2.$$

2001:62A:4:41C:B580:3333:57FA:52FB (talk) 13:46, 24 August 2017 (UTC)

Deleted from to-do list
I deleted the last paragraph, starting with "To simplify the AdSCFT correspondence it is like...", which was a very bad analogy. Dan Gluck 06:29, 15 September 2006 (UTC)

Automorphism group O(2,n-1)
The article states that AdS space has O(2,n-1) as automorphism group. The article should specify which kind of automorphisms (i.e. automorphisms = isometries of a pseudo-Riemannian manifold). Pierreback 19:15, 25 February 2007 (UTC)


 * Should be clear now, I think. User:Linas (talk) 03:56, 3 November 2013 (UTC)

Wrong def
The definition now says that '\alpha' should be a negative constant, but we have '\alpha^2' in the equation? This is wrong. Pierreback 16:27, 28 February 2007 (UTC)

Sentence
The sentence "Anti de Sitter spacetime has closed time-like loops" uses the term "anti de siter spacetime" for the first time in the article. I guess it should be changed to "anti de sitter space". Also, an explanation of "closed time-like loops" should be added. 83.253.30.214 11:27, 21 July 2007 (UTC)


 * Ok; I've added some info about closed timelike loops, and some more links. Ben Standeven 17:09, 23 July 2007 (UTC)

Conformal boundary
Does anybody have some good mathematical definition concerning the conformal boundary? This should be added.

"In the limit as y = 0, this reduces to a Minkowski metric $$dy^2=\left(dt^2-\sum_idx_i^2\right)$$; thus, the anti-de Sitter space contains a conformal Minkowski space at infinity ("infinity" having y-coordinate zero in this patch)."

83.253.30.214 11:34, 21 July 2007 (UTC)

AdS_n
Can someone write what that notation means? Because here the anti de Sitter space have two parameters. 200.145.112.189 (talk) 22:45, 18 November 2009 (UTC)

what the hell does this mean?
"...is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analogue of n-dimensional hyperbolic space, just as Minkowski space and de Sitter space are the analogues of Euclidean and elliptical spaces respectively."

did you write this in some weird language by mistake, because I CANNOT MAKE HEADS OR TAILS OF WTF YOUR TALKING ABOUT!!!! —Preceding unsigned comment added by 96.231.28.194 (talk) 01:17, 2 November 2010 (UTC)

lol... me neither :/. But then I had some oranges and it was k... — Preceding unsigned comment added by 213.42.95.234 (talk) 12:36, 25 March 2012 (UTC)

LOL. Funny, but true. This is an awful lead sentence for an entry into a general encyclopedia. It actually would require great knowledge and effort to distill this into something more accessible [R. Feynman, where have1 you gone?]. 71.208.147.98 (talk) 21:13, 22 July 2014 (UTC)

Capitalisation
I know mid-sentence this is "anti de Sitter space" and not "Anti de Sitter space", but surely the usual laws of grammar apply, and when it's the first word in a sentence, or subheading, it should get a capital "A"? --  Dr Greg   talk  19:47, 9 February 2013 (UTC)
 * Yes. And there should be a hyphen too: anti-de Sitter space. User:Linas (talk) 04:44, 3 November 2013 (UTC)

remove material on AdS/CFT
A large part of the "non-technical" section of this article deals with AdS/CFT ... but we already have a lengthly non-technical article on that. Could someone please cut this section, here? 99.153.64.179 (talk) 04:42, 3 November 2013 (UTC)


 * I moved one sentence to the lead (which I do not endorse), and I nuked the rest. I suspect all of that was written to "translate" some part of the article that no longer exists, having since been moved to the other article. --God made the integers (talk) 07:30, 10 November 2016 (UTC)

Non-technical explanation
I would urge the editors NOT to take out the non-technical section. Most mathematics articles in Wikipedia are USELESS unless you already know the material. This is one of the rare exceptions that offers some non-technical explanations, which are extremely helpful to the non-expert trying to make sense of the more arcane sections.98.170.198.158 (talk) 17:38, 3 April 2014 (UTC)


 * Ugh, well, it's better than nothing but it's still awful. Really, there shouldn't be a section translating the article into english, instead, the article should just be in english. Especially the lead section. I realise this isn't easy. --God made the integers (talk) 06:07, 10 November 2016 (UTC)


 * The tone of the non tech exp is puffy and wordy, yet patronizing. Keep, but rewrite and shorten. 2001:62A:4:41C:B580:3333:57FA:52FB (talk) 14:03, 24 August 2017 (UTC) -


 * Puffy and wordy, a bit, but very helpful. Please don't shorten. RobLandau (talk) 22:31, 8 August 2018 (UTC)

5d interpretation
The 5d interpretation is not quite clear to me. Curvature is an intrinsic property of a manifold. Thus, it appears that the 5d interpretation is not really necessary for anti de Sitter space. The 4d manifold can be embedded in 5d but it seems not necessary and there are many possible embeddings. Is this correct? Should that be mentioned? — Preceding unsigned comment added by 152.3.73.36 (talk) 17:37, 8 December 2014 (UTC)


 * I agree that it is not entirely clear. As I understand it, Anti-deSitter space of any dimension can be embedded in a vector of one extra space-like dimension (but this is not a homogeneous space, since it has a unique origin), where the metric tensor is inherited via the embedding from a Lorentzian quadratic form on the vector space.  Because this is an embedding in a flat space, such an interpretation seems to be a reasonable way to make it understandable.  I do find the wording of the section confusing and possibly not accurate, though, so it could do with some attention. —Quondum 22:14, 8 December 2014 (UTC)


 * I reworded this earlier to at least refer to it as an embedding rather than as a 5-d space, so hopefully at least improved. —Quondum 14:57, 7 July 2016 (UTC)


 * The embedding is total explicit -- it's just the solution of a quadratic equation -- and it gives the metric, not just the topology. See the section above called "Best definition of AdS space?". 2001:62A:4:418:E898:CDB4:21AB:526E (talk) 14:17, 24 August 2017 (UTC)

Simplify intro
The introduction is so complicated, so full of terminology specific to the subject, that it would only make sense to someone who already knows the subject - which makes it worthless to someone trying to learn the subject - which means it is a waste of time in a reference work. At the very least, there needs to be a non-technical thesis statement at the beginning. Pb8bije6a7b6a3w (talk) 17:51, 16 November 2015 (UTC)

"negative" curvature
There is an implicit convention being adopted when calling the curvature of AdS negative. Specifically, the sign of the curvature flips with that of the metric tensor, or (from a physicist's perspective), with which dimensions are labelled spacelike. To refer to the sign of the curvature without stating the convention, or calling out that the sign is not an absolute, is therefore misleading. Surely should be mentioned and if possible sourced?

To make it clearer: AdS2 and dS2 are the same two-dimensional space; they differ only in which dimension is labelled "time" and which is "space". Yet, the curvature is considered to be negative and positive respectively. This ambiguity of convention occurs with all of the spaces AdSp,q. —Quondum 14:54, 7 July 2016 (UTC)


 * We might add something about this, but I'd say that for a "Lorentzian" manifold, yes, true that it can be either (1,n) or (n,1), but whether it's positive or negative, we still call the 1 time. Only the (1,1) case is ambiguous, or the non-Lorentzian cases. --God made the integers (talk) 07:37, 10 November 2016 (UTC)

Incorrect
The sentence "For example, in general relativity, objects in motion have a slightly different gravitation effect than objects at rest." is rubbish. There is no such thing like an "object in motion" or an "object at rest" in general relativity. These notions related to Newtonian absolute space and thus are incorrect ontologies.


 * I agree with this. Even though some (correct) meaning shines through for someone in the know, this sentence is extremely misleading for anybody who reads this for actually seeking information. I'll take it out. WikiPidi (talk) 11:45, 18 November 2019 (UTC)

Nonsense definiton
In the article it is stated $$ S^2 = \frac{O(3)}{O(2)}$$, but it's not at all clear what this means. Clearly it's not a statement about groups because $$ S^2 $$ is not a group, so it must be a statement about diffeomorphisms between topological spaces. But modding manifolds by submanifolds never changes dimensions and as it stands this would say a 3-dimensional thing is homeomorphic to a 2-dimensional thing which is also nonsense. I think the intention is maybe something along the lines of the Hopf map $$ S^1 \hookrightarrow S^3 \twoheadrightarrow S^2$$. I assume something similar holds in the other cases but I have no idea. — Preceding unsigned comment added by INLegred (talk • contribs) 19:46, 27 March 2020 (UTC)


 * $$O(2)$$ is a subgroup of $$O(3)$$ and hence acts on it by left (right) multiplication. I read $$ S^2 = \frac{O(3)}{O(2)}$$ as referring to the quotient space $$O(3)/O(2)$$ of the action of $$O(2)$$ on $$O(3)$$. Shmuel (Seymour J.) Metz Username:Chatul (talk) 06:42, 1 May 2020 (UTC).

Parallel geodesics!
There is no absolute parallelism in GR, only parallel transport along a curve. The phrase parallel geodesic only has meaning when the manifold is parallelizable and a parallelization is specified. I realize that this is a common error in popularizations, but it is still wrong. Shmuel (Seymour J.) Metz Username:Chatul (talk) 06:04, 1 May 2020 (UTC)

Requested move 1 January 2023

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: not moved. (non-admin closure) ModernDayTrilobite (talk • contribs) 17:42, 11 January 2023 (UTC)

Anti-de Sitter space → Anti–de Sitter space – It is impossible to tell from search whether this is usually spelled with a hyphen or an en dash, but MOS:PREFIXDASH calls for an en dash since de Sitter is one name. –LaundryPizza03 ( d c̄ ) 10:28, 1 January 2023 (UTC)
 * Comment – The MoS should be taken with a pinch of salt on this. The hyphen–en dash difference primarily serves to give a cue to disambiguate the semantics of construction.  Unfortunately there are multiple ways of using this and these uses can conflict:
 * Modifier vs. symmetric coupling, e.g. "the paint is green-blue, not blue-green" vs. "the positron–electron annihilation".
 * Implied precedence of grouping of words: a-b–c groups as (a-b)-c vs. a–b-c groups as a-(b-c).
 * Reducing precedence of grouping below a space: a-b c groups as (a-b) c vs. a–b c groups as a-(b c).
 * In the instance "anti-de Sitter space", there is no ambiguity for the average reader, since "anti-de" does not parse. To use an en dash on something that does not need an additional cue then suggests that it may need to be interpreted as a symmetric coupling rather than "anti" being a modifier.  This takes a bit more thinking by the reader to rule out.  Basically, IMO it is less cognitive load to read with a hyphen than with an en dash (it looks odd).  My suggestion would be to make no change, especially as the case to change it is unclear, with any real need for an en dash being removed by there being another cue.  Blindly applying MoS guidelines can produce odd constructions.  —Quondum 19:48, 1 January 2023 (UTC)
 * I browsed through article titles in Physical Review D, and found that of the first 100 search results at, about 3/4 use the en dash when spelling out AdS the title. I could reproduce this fraction for slight variations in the search. –LaundryPizza03 ( d c̄ ) 05:29, 2 January 2023 (UTC)
 * I think what you're seeing is just APS house style. I checked the references that the Wikipedia article is using, and only one used an en-dash instead of an hyphen: the one published by APS. Tercer (talk) 11:22, 2 January 2023 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Oppose I find that the en dash is mainly (in the context of theoretical physics) used to differentiate different names. For example, Kerr–anti-de Sitter should have an en dash, but anti-de Sitter should not and nor should Levi-Civita (as its one person). It feels unhelpful to have two en dashes in Kerr–anti-de Sitter. Of course there are MoS subtleties mentioned above, but I disagree with them being useful or applicable in this case. OpenScience709 (talk) 13:42, 3 January 2023 (UTC)

Recent move
has just moved this page to "Anti–de Sitter space", directly contradicting the result of the requested move from last month. Please respect the consensus and kindly undo the move. Tercer (talk) 15:38, 15 February 2023 (UTC)


 * Sorry, I didn't catch the move request before I made the change. But I think there's still a case to be made as to why MOS:PREFIXDASH shouldn't be overruled here. As stated above, the primary reason is because "de Sitter" is made up of two words, and a hyphen is seen to link only two words on either side of it. It's true that "anti-de" won't be meaningful for the majority of readers, but for those who don't know who de Sitter was and might think that "de" is an abbreviation for some physical concept, the use of an en dash can helpfully clarify the intended meaning. Just because it might feel strange doesn't mean that it's inherently incorrect or unpreferable. If it's good enough for APS journals and their (professional) readers, it should be good enough for us too – like them, we also have a house style to follow.
 * Also: one oppose !vote does not exactly a consensus make. At best, there was a lack of consensus to move the page, but I argue that the default position is that the MOS should apply, and any discussion ought to be on whether it shouldn't. Thanks — <span style="font-family:'Linux Libertine','Georgia','Times',serif"> RAVEN PVFF   · talk  · 14:56, 16 February 2023 (UTC)
 * I'm skeptical that the en-dash can clarify anything, the vast majority of readers won't even notice that there is an en-dash there instead of a hyphen. I participated in the move discussion, and did not bother to !vote oppose because even the proposer seemed to have given up on it. also posted a negative comment but did not !vote. Perhaps they would like to clarify here, and we might have 3 opposing !votes and none supporting, which is clearly a consensus for me.
 * My reasoning is that the references almost exclusively use the hyphen, and we should only deviate from the references for a very good reason. And this does not make the cut, it has very little relevance. Tercer (talk) 16:26, 16 February 2023 (UTC)
 * Reviewing Google Scholar hits, the hyphen dominates – in fact, the only use of the en dash appears to be in APS publications, suggesting a zealous editor (APS also seems to use the hyphen, and even the occasion em dash). "If it's good enough for APS journals ..." just does not cut it as a reason when they are by far the minority exception.  If one looks at the arXiv preprints of the APS papers, one also sees a pattern: the authors use a hyphen, not an en dash, and so it is clear that the en dash is effectively absent among authors, and is introduced by APS style.  If usage is a criterion, then there is a strong case against the en dash.  As for "those who don't know who de Sitter was and might think that 'de' is an abbreviation for some physical concept", no, no, no.  That level of "don't know" can only last for a split second.  We are not interested in helping those who are not interested in the topic and are looking at article titles purely as word salad.  I also agree with 's point: there are commonly expected constructions where we would need to change it to a hyphen anyway to manage of word grouping precedence (including agreeing that usual reasons for using an en dash are inapplicable here, but maybe I was not clear enough that this was what I was saying in my original comment).  Count me as a strong supporter of Tercer's perspective, and a !vote for retaining the hyphen rather than the en dash.  —Quondum 20:34, 16 February 2023 (UTC)
 * My position remains unchanged due to the aforementioned reasoning (and also the reasoning provided above) and is in favor of retaining the hyphen. OpenScience709 (talk) 09:37, 17 February 2023 (UTC)

, as you see there's a clear consensus against the en-dash. Please undo your move. Tercer (talk) 09:23, 21 February 2023 (UTC)


 * As requested. — <span style="font-family:'Linux Libertine','Georgia','Times',serif"> RAVEN PVFF   · talk  · 12:39, 21 February 2023 (UTC)
 * Thanks, much appreciated. Tercer (talk) 12:44, 21 February 2023 (UTC)

rolled vs unrolled
"Some authors define anti-de Sitter space as equivalent to the embedded quasi-sphere itself, while others define it as equivalent to the universal cover of the embedding." This seems very important and should not be buried. --99.238.150.103 (talk) 18:08, 10 September 2023 (UTC)