1109.4254 (Mehmet Akyol et al.)

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

Mehmet Akyol, George Papadopoulos

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. The near horizon geometries preserving 8 supersymmetries
are locally isometric to either $AdS_3\times S^3$ or $\bR^{1,1}\times T^4$.
Moreover, we show that the $\bR^{1,1}\times {\cal S}$ horizons preserve 1, 2
and 4 supersymmetries and the geometry of ${\cal S}$ is Riemann, K\"ahler and
hyper-K\"ahler, respectively.

View original: http://arxiv.org/abs/1109.4254