Study of multi black hole and ring singularity apparent horizons

Details Study of multi black hole and ring singularity apparent horizons Study of multi black hole and ring singularity apparent horizons

2010-08-11

arxiv.org/abs/1008.2001v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, 21 figures

Scientific paper

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 $20/(3\pi) M$. We briefly discuss the connection of this two cases through a discrete black hole 'necklace' configuration.

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