Getting the AdS metric from maximally symmetric spaces

+ 2 like - 0 dislike
49 views

I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. Similarly, how do I get the Poincare patch of $AdS_{p+2}$ i.e $$ds^2 = R^{2}\left(\frac{du^2}{u^2}+u^2(-dt^2+d\mathbf{x}^2)\right)$$ by using the property of maximal symmetry only.

This post imported from StackExchange Physics at 2014-07-28 11:15 (UCT), posted by SE-user Debangshu
asked Nov 1, 2012
It's the same metric written in different coordinates - well, coordinates that only cover the patch. So if you can prove the maximum symmetry in one, the appropriate coordinate transformation proves the maximum symmetry in the other coordinate system or form as well. They're locally the same geometry.

This post imported from StackExchange Physics at 2014-07-28 11:15 (UCT), posted by SE-user Luboš Motl

 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): Email me at this address if my answer is selected or commented on: 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:p$\varnothing$ysicsOverflowThen 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). To avoid this verification in future, please log in or register.