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Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence

Luis Lehner·Nigel T. Bishop·Roberto Gómez·Béla Szilágyi·Jeffrey Winicour
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Abstract

We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as a bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time.

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Luis Lehner, Nigel T. Bishop, Roberto Gómez, Béla Szilágyi, Jeffrey Winicour. 1999-05-26. Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence. https://doi.org/10.1103/physrevd.60.044005

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