  We consider non-expanding shear free (NE-SF) null surface geometries
embeddable as extremal Killing horizons to the second order in Einstein vacuum
spacetimes. A NE-SF null surface geometry consists of a degenerate metric
tensor and a consistent torsion free covariant derivative. We derive the
constraints implied by the existence of an embedding. The first constraint is
well known as the near horizon geometry equation. The second constraint we find
is new. The constraints lead to a complete characterization of those NE-SF null
geometries that are embeddable in the extremal Kerr spacetime. Our results are
also valid for spacetimes with a cosmological constant.

General Relativity and Quantum Cosmology