# Einstein–Weyl spaces and near-horizon geometry

Dunajski, Maciej Lukasz ; Gutowski, J ; Sabra, W (2017-02-02)

Article

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 $\textit{S}$$^\textit{1} X \textit{S}$$^\textit{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.