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No-horizon theorem for spacetimes with spacelike G1 isometry groups

Sergio M. C. V. Goncalves
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Abstract

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.

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Sergio M. C. V. Goncalves. 2003-12-30. No-horizon theorem for spacetimes with spacelike G1 isometry groups. https://doi.org/10.1088/0264-9381%2F20%2F24%2F012

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