Cosmic hoop conjecture?

We propose a hoop conjecture in the presence of a positive cosmological constant Λ: when an apparent horizon forms in a gravitational collapse, the matter must be sufficiently compactified such that the circumference scrC satisfies the condition scrC≲4πM≲4π${\mathit{M}}_{\mathrm{crit}}$, where M is the Abbott-Deser mass of the collapsed body and ${\mathit{M}}_{\mathrm{crit}}$=1/3 √Λ . To confirm our conjecture, we investigate two cases: (1) initial data of a prolate or oblate dust spheroid, and (2) the Kastor-Traschen spacetime which describes a black hole collision with Λ. We also discuss a relation between the hoop conjecture and an appearance of a naked singularity.