Quantum critical collapse abhors a naked singularity
Phys. Rev. D 113, 104029 – Published 13 May, 2026
DOI: https://doi.org/10.1103/7rkc-hmxd
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 qualitatively changes this outcome by dressing the singularity with a horizon within a controlled semiclassical regime. In analytically tractable Einstein-scalar critical spacetimes, a one-loop -wave treatment linearized around self-similar backgrounds shows that regularity uniquely selects an asymptotically Minkowskian, vacuum polarization state. Its renormalized stress tensor carries a universal quantum growing mode that competes with the classical unstable mode, shifts the critical point, and generates a trapped surface along with 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 mass gap truncates the low-mass tail, suggesting potentially important consequences for the predicted mass spectrum. These results provide a self-consistent semiclassical treatment of critical collapse and yield sharp predictions within the one-loop, near-critical, linearized regime.