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We describe the null geometry of a multiple black hole event horizon in termsof a conformal rescaling of a flat space null hypersurface. For the prolatespheroidal case, we show that the method reproduces the pair-of-pants shapedhorizon found in the numerical simulation of the head-on-collision of blackholes. For the oblate case, it reproduces the initially toroidal event horizonfound in the numerical simulation of collapse of a rotating cluster. Theanalytic nature of the approach makes further conclusions possible, such as abearing on the hoop conjecture. From a time reversed point of view, theapproach yields a description of the past event horizon of a fissioning whitehole, which can be used as null data for the characteristic evolution of theexterior space-time.Comment: 21 pages, 6 figures, revtex, to appear in Phys. Rev.

Exact solutions for the intrinsic geometry of black hole coalescence