Toric Sasaki-Einstein metrics on S2×S3

We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski-Demianski metrics one obtains a family of local toric Kähler-Einstein metrics. These can be used to construct local Sasaki-Einstein metrics in five dimensions which are generalisations of the Yp,q manifolds. In fact, we find that these metrics are diffeomorphic to those recently found by Cvetic, Lu, Page and Pope. We argue that the corresponding family of smooth Sasaki-Einstein manifolds all have topology S2×S3. We conclude by setting up the equations describing the warped version of the Calabi-Yau cones, supporting (2,1) three-form flux.