Quantum Critical Collapse Abhors a Naked Singularity

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Abstract
Classical critical collapse yields naked singularities from smooth initial data, challenging cosmic censorship and shaping the spectrum of primordial black holes. We show that one-loop vacuum polarization near the threshold alters this outcome. In analytically tractable Einstein-scalar critical spacetimes, regularity uniquely selects a Boulware-like state whose stress tensor supplies a universal quantum growing mode. Its backreaction competes with the classical unstable mode, producing a shift of the critical point and a finite mass gap at the new threshold, thereby enforcing horizon formation even under arbitrary fine-tuning. In primordial collapse, the threshold shift enters exponentially into the formation fraction, while the gap truncates the low-mass tail -- effects that may reshape the predicted mass spectrum. These results provide the first consistent quantum treatment of critical collapse, offering definitive predictions for several long-standing problems.

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