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 = GM/R is above a numerically determined critical value C > 0.035, we find that imparting a small initial boost counterintuitively prevents the formation of black holes even if C > 0.035. If the boost is further increased, at very high boosts γ > 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 ≈ 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.