Einstein-Weyl spaces and near-horizon geometry

We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three-dimensional Einstein-Weyl structures of hyper-CR type. We characterise this class as most general near-horizon limits of supersymmetric solutions to the five-dimensional theory. In particular we deduce that a compact spatial section of a horizon can only be a Berger sphere, a product metric on S(1)xS(2) or a flat three-torus. We then consider the problem of reconstructing all supersymmetric solutions from a given near-horizon geometry. By exploiting the ellipticity of the linearised field equations we demonstrate that the moduli space of transverse infinitesimal deformations of a near-horizon geometry is finite-dimensional.