Talk:Anti de Sitter space

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Geometry guy 01:34, 15 June 2007 (UTC)

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Help with this template Comments: edit – history – watch – refresh Geometry guy 01:34, 15 June 2007 (UTC)

To-do list for Anti de Sitter space:	edit · history · watch · refresh
Tasks for expert: completely reorganize existing material and add new material, making sure to start with introduction comprehensible to general audience and gradually raising technical ante as needed (wherever possible, link to existing background articles to help guide newbies to places where they can read about some of the neccessary background), in discussion, carefully distinguish between 3+1 and general case, discuss the difference between anti de sitter space (which is NOT simply connected) and the universal cover of anti de sitter space alternative coordinate charts, esp. in 3+1 case, different models: hyperboloid model, upper half-space model static and other observers in 3+1, global properties, esp. in 3+1, add best possible citations to books and review articles, e.g. to classic discussion in Hawking & Ellis (for 3+1 case); avoid citing research papers if there is a review paper which can be cited instead! much better discussion (with citations) of connections with AdS/CFT stuff, in particular, delete or explain the figure (track down author and demand action?) define and discuss the boundary at infinity of anti de Sitter space Note: adding references and better organization should address concern raised by whoever added "technical" flag. Tasks for anyone: spell checking, grammatical and diction corrections, help ensure any citations are in proper format, be careful in wikification to link to proper article (such decisions might require "expert" knowledge)

To-do list for Anti de Sitter space:

edit · history · watch · refresh

Tasks for expert:

completely reorganize existing material and add new material, making sure to start with introduction comprehensible to general audience and gradually raising technical ante as needed (wherever possible, link to existing background articles to help guide newbies to places where they can read about some of the neccessary background),
in discussion, carefully distinguish between 3+1 and general case,
discuss the difference between anti de sitter space (which is NOT simply connected) and the universal cover of anti de sitter space
alternative coordinate charts, esp. in 3+1 case,
different models: hyperboloid model, upper half-space model
static and other observers in 3+1,
global properties, esp. in 3+1,
add best possible citations to books and review articles, e.g. to classic discussion in Hawking & Ellis (for 3+1 case); avoid citing research papers if there is a review paper which can be cited instead!
much better discussion (with citations) of connections with AdS/CFT stuff,
in particular, delete or explain the figure (track down author and demand action?)
define and discuss the boundary at infinity of anti de Sitter space

Note: adding references and better organization should address concern raised by whoever added "technical" flag.

Tasks for anyone:

spell checking, grammatical and diction corrections,
help ensure any citations are in proper format,
be careful in wikification to link to proper article (such decisions might require "expert" knowledge)

This article may be too technical for most readers to understand, and needs attention from an expert on its subject. Please expand it to make it accessible to non-experts, without removing the technical details.

1 Article needs much work
2 half-space chart
3 References
4 Geodesic boundary
5 Blank image
6 Best definition of AdS space?
7 Deleted from to-do list
8 Automorphism group O(2,n-1)
9 Wrong def
10 Sentence
11 Conformal boundary

[edit] 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)

[edit] 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)

[edit] 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)

[edit] Geodesic boundary

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

[edit] 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)

[edit] 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 as 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 $R n + 2$ .

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)."