No-horizon theorem for spacetimes with spacelike G1 isometry groups

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We consider four-dimensional spacetimes (M,g) which obey the Einstein equations G=T, and admit a global spacelike G₁=R isometry group. By means of dimensional reduction and local analyis 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 violations of strong cosmic censorship.