No-horizon theorem for spacetimes with spacelike G1 isometry groups

We consider four-dimensional spacetimes (M, g) which obey the Einstein equations G = T and admit a global spacelike G1 =Risometry group. By means of dimensional reduction and local analysis on the reduced (2 + 1) spacetime, we obtain a sufficient condition on T which guarantees that (M, g) cannot contain apparent horizons. Given any (3 + 1) spacetime with spacelike translational isometry, the no-horizon condition can be readily tested without the need for dimensional reduction. This provides thus a useful and encompassing apparent horizon test for G1-symmetric spacetimes. We argue that this adds further evidence towards the validity of the hoop conjecture and signals possible (albeit arguably unlikely) violations of strong cosmic censorship.