Topology and geometry of 6-dimensional (1,0) supergravity black hole horizons

Understand

We show that the supersymmetric near horizon black hole geometries of 6-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally $AdS_3\times \Sigma^3$, where \Sigma^3 is a homology 3-sphere, or $\bR^{1,1}\times {\cal S}^4$, where ${\cal S}^4$ is a 4-manifold whose geometry depends on the hypermultiplet scalars.

• In both cases, we find that the tensorini multiplet scalars are constant and the associated 3-form field strengths vanish.
• We also demonstrate that the $AdS_3\times \Sigma^3$ horizons preserve 2, 4 and 8 supersymmetries.
• For horizons with 4 supersymmetries, \Sigma^3 is in addition a non-trivial circle fibration over a topological 2-sphere.