The classification of static electro--vacuum space--times containing an asymptotically flat spacelike hypersurface with compact interior

We show that static electro--vacuum black hole space--times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non--degenerate components of the event horizon do not exist. This is done by a careful study of the near-horizon geometry of degenerate horizons, which allows us to eliminate the last restriction of the static electro-vacuum no-hair theory.