Static M-horizons

TL;DR

This paper classifies static black hole horizons in M-theory preserving supersymmetry, revealing their geometric structures and deriving conditions for specific cases involving Spin(7) and SU(4) structures.

Contribution

It provides a complete geometric classification of static supersymmetric horizons in M-theory, including explicit conditions and examples for Spin(7) and SU(4) structures.

Findings

All such horizons are warped products of R^{1,1} or AdS_2 with a spatial section S.

Electric static horizons with Spin(7) structure have a Spin(7) holonomy manifold as S.

Electric static solutions with SU(4) structure include AdS_2 * S^3 * CY_6 and other constructions.

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 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 * S^3 * CY_6 as well as many others constructed from taking the 8-dimensional Kahler manifold to be a product of Kahler-Einstein and Calabi-Yau spaces.