An Infinite Class of Extremal Horizons in Higher Dimensions

We present a new class of near-horizon geometries which solve Einstein's vacuum equations, including a negative cosmological constant, in all even dimensions greater than four. Spatial sections of the horizon are inhomogeneous S^2-bundles over any compact Kaehler-Einstein manifold. For a given base, the solutions are parameterised by one continuous parameter (the angular momentum) and an integer which determines the topology of the horizon. In six dimensions the horizon topology is either S^2 x S^2 or CP^2 # -CP^2. In higher dimensions the S^2-bundles are always non-trivial, and for a fixed base, give an infinite number of distinct horizon topologies. Furthermore, depending on the choice of base we can get examples of near-horizon geometries with a single rotational symmetry (the minimal dimension for this is eight). All of our horizon geometries are consistent with all known topology and symmetry constraints for the horizons of asymptotically flat or globally Anti de Sitter extremal black holes.Comment: 42 pages, latex. v2: corrected section 6.1, two references added. v3: modified angular momentum and corrected area comparison, version to be published in Commun. Math. Phy