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

TL;DR

This paper proves that (3+1) vacuum spacetimes with a global spacelike translational symmetry cannot contain apparent horizons, extending the hoop conjecture to such symmetric vacuum solutions.

Contribution

It establishes a no-horizon theorem for vacuum spacetimes with a global spacelike G1 isometry group, under minimal assumptions.

Findings

Vacuum spacetimes with spacelike G1 symmetry lack apparent horizons.

The result applies broadly to arbitrary metrics with the given symmetry.

Supports the hoop conjecture in the context of symmetric vacuum solutions.

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.