Einstein--Weyl Spaces and Near-Horizon Geometry

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.

References in corpus (13)

• All supersymmetric solutions of minimal supergravity in five dimensions
• Higher dimensional black holes and supersymmetry
• Classification of near-horizon geometries of extremal black holes
• A generalization of Hawking's black hole topology theorem to higher dimensions
• A class of Einstein--Weyl spaces associated to an integrable system of hydrodynamic type
• Symmetries of Higher Dimensional Black Holes
• Extremal Isolated Horizons: A Local Uniqueness Theorem
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality
• Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs
• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• Transverse deformations of extreme horizons
• Index Theory and Supersymmetry of 5D Horizons
• On supersymmetric Einstein-Weyl spaces

Cited by in corpus (16)

• Einstein manifolds with torsion and nonmetricity
• Schrödinger connection with selfdual nonmetricity vector in 2+1 dimensions
• An action principle for the Einstein-Weyl equations
• The Maxwell-Chern-Simons gravity and its cosmological implications
• Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spaces
• Uniqueness of the extremal Schwarzschild de Sitter spacetime
• Electrovacuum spacetime near an extreme horizon
• Moduli Spaces of Transverse Deformations of Near-Horizon Geometries
• Spinorial geometry, off-shell Killing spinor identities and higher derivative 5D supergravities
• Parallel spinors on Lorentzian Weyl spaces
• Uniqueness of extremal charged black holes in de Sitter
• Existence and Uniqueness of Near-Horizon Geometries for 5-Dimensional Black Holes
• Rigidity of the extremal Kerr-Newman horizon
• Solutions of D=4 Gauged Pseudo-Supergravity
• Recurrent Lorentzian Weyl spaces
• Lie point symmetries of near-horizon geometry equation