Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.