We start with the general case of AdSp+2 i.e AdS space in p+2 dimension.
X20+X2p+2−p+1∑i=1X2i=R2
This space has an isometry
SO(2,p+1) and is homogeneous and isotropic. The Poincare Patch is given by
ds2=R2(du2u2+u2(−dt2+dx2))
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