Extremal Sasakian horizons

TL;DR

The paper presents a straightforward method to construct an infinite family of Einstein near-horizon geometries in odd dimensions above five, with horizon cross-sections modeled by inhomogeneous Sasakian metrics on certain manifolds.

Contribution

It introduces a simple construction of Einstein near-horizon geometries with inhomogeneous Sasakian cross-sections in higher odd dimensions, expanding known solutions.

Findings

Constructed infinite classes of Einstein near-horizon geometries.

Horizon cross-sections are inhomogeneous Sasakian manifolds.

Results align with topology and symmetry constraints for black holes.

Abstract

We point out a simple construction of an infinite class of Einstein near-horizon geometries in all odd dimensions greater than five. Cross-sections of the horizons are inhomogeneous Sasakian metrics (but not Einstein) on S^3xS^2 and more generally on Lens space bundles over any compact positive Kaehler-Einstein manifold. They are all consistent with the known topology and symmetry constraints for asymptotically flat or globally AdS black holes.