ABSENCE OF APPARENT HORIZONS IN TRANSLATIONALLY-INVARIANT EINSTEIN–MAXWELL SPACETIMES

We show that (3+1) Einstein–Maxwell 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 spacetime metric is otherwise completely arbitrary. We discuss the implications of this result for the hoop and cosmic censorship conjectures.