Ultra Relativistic Particle Collisions

TL;DR

It is shown for the first time that at sufficiently high energies the collision leads to black hole formation, consistent with hoop-conjecture arguments, which implies that the nonlinear gravitational interaction between the kinetic energy of the solitons causes gravitational collapse, and that arguments forblack hole formation in super-Planck scale particle collisions are robust.

Abstract

We present results from numerical solution of the Einstein field equations describing the head-on collision of two solitons boosted to ultra relativistic energies. We show, for the first time, that at sufficiently high energies the collision leads to black hole formation, consistent with hoop conjecture arguments. This implies that the non-linear gravitational interaction between the kinetic energy of the solitons causes gravitational collapse, and that arguments for black hole formation in super-Planck scale particle collisions are robust.

Figures (2)

• Figure 1: Magnitude $|\phi|$ of the scalar field from 4 different simulations, in 4 panels (left to right). The 4 sub-panels within each panel depict $|\phi|$ at different times as follows (top to bottom): 1) $t/M_0=0$, 2) a time at which the boson stars first completely overlap, 3) a short time later when $|\phi|$ reaches a first local maximum due to gravitational focusing, 4) a late time after the collision. The axis of symmetry is coincident with the top edge of each sub-panel. The insets, where present, are zoom-ins of the central interaction regions. For the $\gamma=4$ case, a black hole forms near the time of sub-panel 3---the black line in the corresponding inset shows the shape of the apparent horizon then, and the black semi-circle in sub-panel 4 is the excised region inside the black hole.
• Figure 2: $\Psi_4$ at $t=540M_0$ on the plane passing through the collision point and orthogonal to the axis, for two cases.