No-horizon theorem for spacetimes with spacelike G1 isometry groups

We consider four-dimensional spacetimes $(M,\mathbf{g})$ which obey the Einstein equations $\mathbf{G}=\mathbf{T}$, and admit a global spacelike $G_1=\mathbb{R}$ isometry group. By means of dimensional reduction and local analyis on the reduced (2+1) spacetime, we obtain a sufficient condition on $\mathbf{T}$ which guarantees that $(M,\mathbf{g})$ 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 $G_1$-symmetric spacetimes. We argue that this adds further evidence towards the validity of the hoop conjecture, and signals possible violations of strong cosmic censorship.