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No-horizon theorem for vacuum gravity with spacelike G1 isometry groups

Sergio M. C. V. Goncalves
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Abstract

We show that (3+1) vacuum 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 vacuum spacetime metric is otherwise arbitrary. This result may thus be viewed as a hoop conjecture theorem for vacuum gravity with one spacelike translational Killing symmetry.

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Sergio M. C. V. Goncalves. 2003-12-30. No-horizon theorem for vacuum gravity with spacelike G1 isometry groups. https://doi.org/10.1103/physrevd.68.101502

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