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Mathematics Start‑class Low‑priority

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This topic is in need of attention from an expert on the subject.

The section or sections that need attention may be noted in a message below.

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)[reply]

Article needs much work

This article should probably be split:

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,
the four dimensional example, with discussion of nice coordinate charts as in Hawking and Ellis

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)[reply]

half-space chart

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

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)[reply]

References

It would be very nice with some references to some expository article (or book?). (unsigned comment by 130.238.149.247)

Indeed yes. Someone removed the expert flag I am now restoring. I am adding a short todo list which will include your request. ---CH 19:46, 5 February 2006 (UTC)[reply]

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)[reply]

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)[reply]

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. [[1]] .

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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

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)[reply]

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)[reply]

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

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 $dy^{2}=\left(dt^{2}-\sum _{i}dx_{i}^{2}\right)$ ; 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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

Yes. And there should be a hyphen too: anti-de Sitter space. User:Linas (talk) 04:44, 3 November 2013 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

"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 AdS_p,q. —Quondum 14:54, 7 July 2016 (UTC)[reply]

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)[reply]

@@ Line 70: / Line 70: @@
 be as the solution to the equation
 :<math>x_1^2 + x_2^2 + \cdots + x_n^2 - x_{n+1}^2 - x_{n+2}^2 = -1, </math>
-which is a one-sheeted hyperboloid in <math>R^{n+2}</math>. It becomes a Lorentz manifold by restricting to it the ambient metric <math>g</math> of signature (n,2) given by
+which is a one-sheeted hyperboloid in <math>R^{n+2}.</math> It has the topology of <math>R^n\times S^1.</math> It becomes a Lorentz manifold, with the <math>S^1</math> timelike, by restricting to it the ambient metric <math>g</math> of signature (n,2) given by
-:<math>g = dx_1^2 + dx_2^2 + \cdots + dx_n^2 - dx_{n+1}^2 - dx_{n+2}^2 </math>
+:<math>g = dx_1^2 + dx_2^2 + \cdots + dx_n^2 - dx_{n+1}^2 - dx_{n+2}^2.</math>
 [[Special:Contributions/2001:62A:4:41C:B580:3333:57FA:52FB|2001:62A:4:41C:B580:3333:57FA:52FB]] ([[User talk:2001:62A:4:41C:B580:3333:57FA:52FB|talk]]) 13:46, 24 August 2017 (UTC)