Constructing near-horizon geometries in supergravities with hidden symmetry

We consider the classification of near-horizon geometries in a general two-derivative theory of gravity coupled to abelian gauge fields and uncharged scalars in four and five dimensions, with one and two commuting rotational symmetries respectively. Assuming that the theory of gravity reduces to a 3d non-linear sigma model (as is typically the case for ungauged supergravities), we show that the functional form of any such near-horizon geometry may be determined. As an example we apply this to five dimensional minimal supergravity. We also construct an example of a five parameter near-horizon geometry solution to this theory with S^1 X S^2 horizon topology. We discuss its relation to the near-horizon geometries of the yet to be constructed extremal black rings with both electric and dipole charges.
Comment: Latex, 30 pages. v2: discussion in section 5 modified and improved, other minor changes, references added