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 $mathcal{C}equiv GM/R$ is above a numerically determined critical value $mathcal{C}>0.035$, we find that imparting a small initial boost counter-intuitively emph{prevents} the formation of black holes even if $mathcal{C}> 0.035$. If the boost is further increased, at very high boosts $gamma>1/12mathcal{C}$, 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 ${cal C}approx 0.07$. 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.
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