Toric Kahler metrics and AdS5 in ring-like co-ordinates
Bobby S. Acharya, Suresh Govindarajan, Chethan N. Gowdigere
Abstract
Stationary, supersymmetric supergravity solutions in five dimensions have Kahler metrics on the four-manifold orthogonal to the orbits of a time-like Killing vector. We show that an explicit class of toric Kahler metrics provide a unified framework in which to describe both the asymptotically flat and asymptotically AdS solutions. The Darboux co-ordinates used for the local description turn out to be ''ring-like.'' We conclude with an Ansatz for studying the existence of supersymmetric black rings in AdS.
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