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We investigate the validity of Thorne's hoop conjecture in non-axisymmetricspacetimes by examining the formation of apparent horizons numerically. Ifspaces have a discrete symmetry about one axis, we can specify the boundaryconditions to determine an apparent horizon even in non-axisymmetric spaces. Weimplement, for the first time, the ``hoop finder'' in non-axisymmetric spaceswith a discrete symmetry. We construct asymptotically flat vacuum solutions ata moment of time symmetry. Two cases are examined: black holes distributed on aring, and black holes on a spherical surface. It turns out that calculating${\cal C}$ is reduced to solving an ordinary differential equation. We findthat even in non-axisymmetric spaces the existence or nonexistence of anapparent horizon is consistent with the inequality: ${\cal C} \siml 4\pi M$.Comment: 18 pages, typos fixed, to be published in Phys.Rev.

Apparent horizon formation and hoop conjecture in nonaxisymmetric spaces