Einstein--Weyl Spaces and Near-Horizon Geometry

TL;DR

This paper classifies near-horizon geometries of supersymmetric solutions in five-dimensional minimal supergravity, linking them to Einstein--Weyl structures and analyzing their deformation space.

Contribution

It characterizes the most general near-horizon limits of supersymmetric solutions and explores the moduli space of their deformations, connecting geometric structures to supergravity solutions.

Findings

Compact horizon sections are limited to Berger spheres, $S^1\times S^2$, or flat tori.

The moduli space of deformations is finite-dimensional.

Near-horizon geometries correspond to lifts of hyper-CR Einstein--Weyl structures.

Abstract

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 $S^1\times S^2$ 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.