Degenerate horizons, Einstein metrics, and Lens space bundles

TL;DR

This paper introduces a new class of near-horizon geometries with degenerate horizons in odd dimensions, featuring Lens space bundle topologies, expanding the understanding of Einstein metrics and black hole horizon structures.

Contribution

It constructs an infinite family of Einstein near-horizon geometries with Lens space bundle topologies in all odd dimensions greater than five, unifying known examples.

Findings

New infinite class of near-horizon geometries in odd dimensions

Horizon topologies include S^3xS^2 and Lens space bundles

Unified family of Einstein metrics on Lens space bundles

Abstract

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 S^3xS^2 or the non-trivial S^3-bundle over S^2. More generally, the horizons are Lens space bundles associated to certain principal torus-bundles over Fano Kaehler-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).