  We show that (3+1) vacuum spacetimes admitting a global, spacelike,
one-parameter Lie group of isometries of translational type cannot contain
apparent horizons. The only assumption made is that of the existence of a
global spacelike Killing vector field with infinite open orbits; the
four-dimensional vacuum spacetime metric is otherwise arbitrary. This result
may thus be viewed as a hoop conjecture theorem for vacuum gravity with one
spacelike translational Killing symmetry.
