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,R-1 x(w) S or AdS(2) X-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,R-1 x 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 Kahler manifold which satisfies an additional condition involving the Ricci scalar and the length of the Ricci tensor. Solutions include AdS(2) x S-3 x CY6 as well as many others constructed from taking the 8-dimensional Kahler manifold to be a product of Kahler-Einstein and spaces.
|Journal of High Energy Physics
|Published - 2012