3D Numerical Simulation of Black Hole Formation Using Collisionless Particles

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Abstract
We have constructed a numerical code for 3D numerical relativity with which we can investigate black hole formation processes for a wide variety of problems. We adopt a standard 3+1 formalism for the evolution of geometric variables incorporating a swarm of collisionless particles as a source of the energy momentum tensor. In order to determine black hole formation, we also incorporate an apparent horizon finder which was recently developed. Assuming triplane symmetries with respect to x−y, y−z and z−x planes, we have performed a variety of simulations for black hole formation, such as the collapse of triaxial ellipsoids, collapse of spheroids of co-rotating and counter-rotating particles, and head-on collision of two nearly equilibrium spherical clusters, as well as test-bed simulations including spherical symmetric dust collapse. We present numerical results and demonstrate that using our numerical code, we can investigate black hole formation in these problems fairly accurately.

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