Hoop conjecture for black-hole horizon formation

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Abstract
The hoop conjecture was proposed by Thorne in 1972 as a loosely formulated, necessary, and sufficient condition for the formation of a horizon in nonspherical gravitational collapse. In this paper we discuss some issues that arise in formulating various precise interpretations of the conjecture, and review some of the small amount of literature that has appeared on this subject. We further specialize the conjecture to static, vacuum, axisymmetric spacetimes and show that it is satisfied in three particular cases of such spacetimes. We also prove a theorem for oblate geometries giving a sufficient condition for the conjecture to be satisfied.