Non-degenerate Killing horizons in analytic vacuum spacetimes

I will present a geometric characterization of all possible 4-dimensional real analytic vacuum spacetimes near non-degenerate Killing horizons. This 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. This is joint work with Klaus Kröncke.