3D Simulation of Spindle Gravitational Collapse of a Collisionless Particle System

Abstract

We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky(ST). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but go well beyond.We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.

Results are updated and new results on horizon formation are added in 2nd version. 19 pages, 10 figures

References in corpus (6)

• Primordial black hole formation in the matter-dominated phase of the Universe
• Observable Spectra of Induced Gravitational Waves from Inflation
• Generating Primordial Black Holes Via Hilltop-Type Inflation Models
• 3+1 geodesic equation and images in numerical spacetimes
• Formation of naked singularities in five-dimensional space-time
• Seeking for toroidal event horizons from initially stationary BH configurations

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• Cylindrical spacetimes due to radial magnetic fields
• Structure formation and quasi-spherical collapse from initial curvature perturbations with numerical relativity simulations
• Dynamical Transition from a Naked Singularity to a Black Hole
• COSMOS: A numerical relativity code specialized for PBH formation