Curvature-Induced Deconfinement near Black Holes: Critical Curvature, Order-Parameter Dynamics, and a No-Go Result for Singularity Resolution by a Non-Minimally Coupled Confinement Order Parameter

More than 99% of the mass of baryonic matter originates in the binding energy of the strong interaction rather than in the Higgs mechanism. This motivates the hypothesis that sufficiently extreme spacetime curvature destroys the confining QCD vacuum before a curvature singularity forms, removing the dominant gravitating source. We develop this hypothesis quantitatively and test whether it can regularize a black hole. Two heuristic estimates—a Tolman–Unruh local-temperature argument and the one-loop Schwinger–DeWitt correction to the gluon condensate—locate the critical curvature at the order-of-magnitude level –, with curvature radius at the hadronic scale ( fm) and  orders of magnitude below the Planck curvature. We stress that these are plausibility estimates rather than precision predictions: the condensate calculation in particular is extrapolated beyond the strict domain of the heat-kernel expansion. We model the confinement order parameter as a  scalar  non-minimally coupled through  and show that it undergoes a continuous second-order transition to the deconfined phase at . We then derive the full static, spherically symmetric Einstein–scalar system, prove that the single-metric-function ansatz is inconsistent, integrate the two-function system from a regular core across a grid of parameters, and find that no regular black hole forms: the field generically overshoots its vacuum and either runs into the conformal singularity at  or drives the metric functions to diverge, so the solution fails to be asymptotically flat. A frame-independent Einstein-frame analysis explains both outcomes: mapping to a canonical scalar shows the model obeys the null energy condition for , so that Bronnikov’s obstruction—that a canonical (non-ghost) scalar cannot source a regular black hole—applies directly. We verify the singularity is genuine by computing the divergence of the Kretschmann invariant. The contribution is therefore not a new gravitational theorem but the demonstration that this physically-motivated QCD scenario reduces to the known no-go case; the deconfinement mechanism is sound, but it cannot by itself resolve the singularity. All results are reproducible from the provided code, data, logs, and regression tests.