It is known that the near horizon limit of a ($d+1$) dimensional extremal charged black hole (BH) is $AdS_2\times S^{d-1}$. I was looking at this paper by Faulkner et al. They consider a ($d+1$) dimensional extremal charged BH (rather black brane) which is asymptotically $AdS$. Now for zero temperature I can use their scaling limits (eqn. (20)) to obtain the $AdS_2\times R^{d-1}$.

Can someone tell me how to use the other scaling limit (eqn. (23)) to obtain the small temperature near horizon limit which is $AdS_2BH\times R^{d-1}$?

I understand this is a bit technical (home work type) question. Any hint or may-be-useful references are be much appreciated!

This post imported from StackExchange Physics at 2015-10-24 21:28 (UTC), posted by SE-user pinu