Ultrarelativistic Particle Collisions

We present results from numerical solution of the Einstein field equations describing the head-on collision of two solitons boosted to ultrarelativistic 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 nonlinear 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.

Figure 1

Magnitude $|\varphi |$ of the scalar field from 4 different simulations, in 4 panels (left to right). The 4 subpanels within each panel depict $|\varphi |$ 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 $|\varphi |$ 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 subpanel. 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 subpanel 3—the black line in the corresponding inset shows the shape of the apparent horizon then, and the black semicircle in subpanel 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.