Study of multi black hole and ring singularity apparent horizons

Understand

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.