Toric Kähler metrics andAdS5in ring-like co-ordinates

Stationary, supersymmetric supergravity solutions in five dimensions haveKahler metrics on the four-manifold orthogonal to the orbits of a time-likeKilling vector. We show that an explicit class of toric Kahler metrics providea unified framework in which to describe both the asymptotically flat andasymptotically AdS solutions. The Darboux co-ordinates used for the localdescription turn out to be ''ring-like.'' We conclude with an Ansatz forstudying the existence of supersymmetric black rings in AdS.Comment: A new appendix derives the explicit co-ordinate transformation between the ``ring-like'' co-ordinates and the polar co-ordinates of global AdS. Also, references adde