Black hole formation in relativistic Oscillaton collisions

We investigate the physics of black hole formation from the head-on collisions of boosted equal mass Oscillatons (OS) in full numerical relativity, for both the cases where the OS have equal phases or are maximally off-phase (anti-phase). While unboosted OS collisions will form a BH as long as their initial compactness $C\equiv GM/R$ is above a numerically determined critical value $C>0.035$, we find that imparting a small initial boost counter-intuitively prevents the formation of black holes even if $C>0.035$. If the boost is further increased, at very high boosts $\gamma >1/12C$, BH formation occurs as predicted by the hoop conjecture. These two limits combine to form a "stability band" where collisions result in either the OS "passing through" (equal phase) or "bouncing back" (anti-phase), with a critical point occurring around $C\approx 0.07$. We argue that the existence of this stability band can be explained by the competition between the free fall and the interaction timescales of the collision.