Rigidity of the extremal Kerr-Newman horizon

TL;DR

This paper proves that extremal horizons in Einstein-Maxwell theory are geometrically constrained to be extremal Kerr-Newman horizons, completing their classification and showing they must admit a Killing vector or be static.

Contribution

It establishes that the intrinsic geometry of extremal horizons necessarily admits a Killing vector or is static, confirming they are extremal Kerr-Newman horizons and extending to include a cosmological constant.

Findings

Extremal horizons in Einstein-Maxwell theory are either static or admit a Killing vector.

All such horizons are classified as extremal Kerr-Newman horizons.

Results hold even with a non-zero cosmological constant.

Abstract

We prove that the intrinsic geometry of compact cross-sections of an extremal horizon in four-dimensional Einstein-Maxwell theory must admit a Killing vector field or is static. This implies that any such horizon must be an extremal Kerr-Newman horizon and completes the classification of the associated near-horizon geometries. The same results hold with a cosmological constant.