No-horizon theorem for spacetimes with spacelike G1 isometry groups

TL;DR

This paper proves a condition under which spacetimes with a spacelike G1 isometry group cannot contain apparent horizons, offering a practical test and implications for cosmic censorship and the hoop conjecture.

Contribution

It introduces a sufficient condition on the energy-momentum tensor that prevents apparent horizons in G1 symmetric spacetimes, enhancing understanding of horizon formation.

Findings

No apparent horizons under certain energy conditions in G1 symmetric spacetimes.

A practical test for horizon absence without dimensional reduction.

Implications for the hoop conjecture and cosmic censorship.

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.