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

31 pages, 21 figures

References in corpus (16)

• Black Holes in Higher Dimensions
• Large Merger Recoils and Spin Flips From Generic Black-Hole Binaries
• Maximum gravitational recoil
• Spin Flips and Precession in Black-Hole-Binary Mergers
• Binary-black-hole initial data with nearly-extremal spins
• Geometry and Regularity of Moving Punctures
• Foundations of multiple black hole evolutions
• Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole Binaries
• Close encounters of three black holes
• Bowen-York trumpet data and black-hole simulations
• Three-body equations of motion in successive post-Newtonian approximations
• Quasi-Local Linear Momentum in Black-Hole Binaries
• Algebraic Classification of Numerical Spacetimes and Black-Hole-Binary Remnants
• Trumpet-puncture initial data for black holes
• Probing the puncture for black hole simulations
• Seeking for toroidal event horizons from initially stationary BH configurations

Cited by in corpus (5)

• On geometry of deformed black holes: I. Majumdar-Papapetrou binary
• Static axisymmetric rings in general relativity: How diverse they are
• Geometric relations for rotating and charged AdS black holes
• Evolution of a black hole cluster in full general relativity
• Extreme Gravitational Interactions in the Problem of Three Black Holes in General Relativity