Study of multi black hole and ring singularity apparent horizons
Abstract
We study critical black hole separations for the formation of a common apparent horizon in systems of N - black holes in a time symmetric configuration. We study in detail the aligned equal mass cases for N=2,3,4,5, and relate them to the unequal mass binary black hole case. We then study the apparent horizon of the time symmetric initial geometry of a ring singularity of different radii. The apparent horizon is used as indicative of the location of the event horizon in an effort to predict a critical ring radius that would generate an event horizon of toroidal topology. We found that a good estimate for this ring critical radius is 20/(3π) M. We briefly discuss the connection of this two cases through a discrete black hole 'necklace' configuration.