  We consider smooth electrovac spacetimes which represent either (A) an
asymptotically flat, stationary black hole or (B) a cosmological spacetime with
a compact Cauchy horizon ruled by closed null geodesics. The black hole event
horizon or, respectively, the compact Cauchy horizon of these spacetimes is
assumed to be a smooth null hypersurface which is non-degenerate in the sense
that its null geodesic generators are geodesically incomplete in one direction.
In both cases, it is shown that there exists a Killing vector field in a
one-sided neighborhood of the horizon which is normal to the horizon. We
thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief
(for case (B)) to the non-analytic case.
