• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

204 submissions , 162 unreviewed
5,030 questions , 2,184 unanswered
5,344 answers , 22,705 comments
1,470 users with positive rep
816 active unimported users
More ...

  Poincare Patch covers half of the hyperboloid of AdS

+ 3 like - 0 dislike

We start with the general case of $AdS_{p+2}$ i.e AdS space in $p+2$ dimension. \begin{equation} X_{0}^{2}+X_{p+2}^{2}-\sum_{i=1}^{p+1}X_{i}^{2} = R^2 \end{equation} This space has an isometry $SO(2,p+1)$ and is homogeneous and isotropic. The Poincare Patch is given by \begin{equation} ds^2 = R^{2}\left(\frac{du^2}{u^2}+u^2(-dt^2 +d\mathbf{x}^{2})\right) \end{equation} According to Equation (2.27) of the article http://arxiv.org/abs/hep-th/9905111, The second metric covers only half of the hyperboloid. Firstly, how do I show this. Secondly, when I go to the asymptotic limit (small radial distance), should the topology of the two spaces be different?

This post imported from StackExchange Physics at 2014-07-28 11:14 (UCT), posted by SE-user Debangshu
asked Nov 16, 2012 in Theoretical Physics by DebangshuMukherjee (165 points) [ no revision ]

1 Answer

+ 1 like - 0 dislike

It can be shown by conformal compactification of the spacetime, i.e. using coordinates which allow you to draw a penrose diagram. After you have done so, you can analytically continue the geometry and discover the other half (see chapter 2 of this) . Regarding differences in topology: I don't see any reason for this to be the case.

This post imported from StackExchange Physics at 2014-07-28 11:14 (UCT), posted by SE-user Frederic Brünner
answered Feb 15, 2013 by Frederic Brünner (1,130 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights