Regular black hole solutions and the quark chemical potential at the QCD phase transition

Motivated by Refs.[1, 2], we investigate whether quantum chromodynamics (QCD)-inspired matter at finite quark chemical potential can dynamically support \emph{regular} black-hole interiors during gravitational collapse. To this end, we couple two effective equations of state, namely a three-flavor chiral quark model at finite temperature and chemical potential and a cold-QGP mean-field model with a dynamical gluon mass, to a spherically symmetric advanced Eddington--Finkelstein geometry. The matter source is treated as an effective anisotropic fluid. Rather than assuming a regular mass profile a priori, we determine the radial temperature dependence from the local conservation law and reconstruct the mass function from the Einstein equations. In the chiral model, the conservation equation admits an exact Lambert-function solution, but the physical coefficients select a singular near-center branch. In the cold-QGP model, the exact implicit temperature-radius relation drives the temperature to diverge near the center, causing the thermodynamic source terms and the reconstructed mass function to become incompatible with the regular-center condition. We therefore find that, within the effective framework adopted here, finite quark chemical potential reshapes the thermodynamics of the collapse phase but does not by itself provide a self-regularizing black-hole core. Any regular completion must invoke an additional inner vacuum-like phase or further microphysics beyond the two QCD-inspired equations of state considered in this work.