  We prove a geometric characterization of all possible 4-dimensional real
analytic vacuum spacetimes near non-degenerate Killing horizons. It is known
that any such horizon admits a canonically induced real analytic Riemannian
metric with a Killing vector field of constant length. In this paper we prove
the converse statement: Every real analytic Riemannian 3-manifold, which admits
a Killing vector field of constant length, gives rise to a unique (up to
isometry) real analytic vacuum spacetime near a non-degenerate Killing horizon.
Our result applies in particular to bifurcate horizons (e.g. black hole event
horizons) and non-degenerate compact Cauchy horizons in real analytic vacuum
spacetimes, since classical results of Hawking and Moncrief-Isenberg (and
recent generalizations thereof) show that such horizons are non-degenerate
Killing horizons.
