Degenerate horizons, Einstein metrics, and Lens space bundles

We present a new infinite class of near-horizon geometries of degenerate horizons, satisfying Einstein’s equations for all odd dimensions greater than five. The symmetry and topology of these solutions is compatible with those of black holes. The simplest examples give horizons of spatial topology S3×S2 or the non-trivial S3-bundle over S2. More generally, the horizons are Lens space bundles associated to certain principal torus-bundles over Fano Kähler–Einstein manifolds. We also consider the classification problem for Einstein metrics on such Lens space bundles and derive a family which unifies all the known examples (Sasakian and non-Sasakian).