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

Non-degenerate Killing horizons in analytic vacuum spacetimes