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

We show that the supersymmetric near horizon black hole geometries of six-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally AdS(3) x Sigma(3), where Sigma(3) is a homology 3-sphere, or R-1,R-1 x S-4, where 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) x Sigma(3) horizons preserve two, four and eight supersymmetries. For horizons with four supersymmetries, Sigma(3) is in addition a non-trivial circle fibration over a topological 2-sphere. The near horizon geometries preserving eight supersymmetries are locally isometric to either AdS(3) x S-3 or R-1,R-1 x T-4. Moreover, we show that the R-1,R-1 x S horizons preserve one, two and four supersymmetries and the geometry of S is Riemann, Kahler and hyper-Kahler, respectively.