Toric Kähler metrics and AdS <inf>5</inf> in ring-like co-ordinates

Stationary, supersymmetric supergravity solutions in five dimensions have Kähler metrics on the four-manifold orthogonal to the orbits of a time-like Killing vector. We show that an explicit class of toric Kähler 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. © SISSA 2007.