Study of multi black hole and ring singularity apparent horizons

TL;DR

This paper investigates the formation of apparent horizons in multi-black hole systems and ring singularities, identifying critical parameters for horizon formation and topology changes, with implications for understanding black hole mergers and ring singularities.

Contribution

It provides new insights into the critical separations for apparent horizon formation in multi-black hole systems and estimates the critical ring radius for toroidal event horizons.

Findings

Critical black hole separation for horizon formation identified.

Estimated critical ring radius for toroidal horizon is approximately 20/(3π) M.

Connection between multi-black hole systems and ring singularities discussed.

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