Static M-horizons

Abstract

We determine the geometry of all static black hole horizons of M-theory preserving at least one supersymmetry. We demonstrate that all such horizons are either warped products R 1,1 × w S or AdS 2 × w S, where S admits an appropriate Spin(7) or SU(4) structure respectively; and we derive the conditions imposed by supersymmetry on these structures. We show that for electric static horizons with Spin(7) structure, the near horizon geometry is a product R 1,1 × S, where S is locally a compact Spin(7) holonomy manifold. For electric static solutions with SU(4) structure, we show that the horizon section S is a circle fibration over an 8-dimensional K̈ahler manifold which satisfies an additional condition involving the Ricci scalar and the length of the Ricci tensor. Solutions include AdS 2×S 3×CY 6 as well as many others constructed from taking the 8-dimensional K̈ahler manifold to be a product of K̈ahler-Einstein and Calabi-Yau spaces. © SISSA 2012.