Can finite-density QCD matter support a regular black hole core?

Abstract

We investigate whether finite-density QCD matter can provide the stress-energy needed to regularize the center of a spherically symmetric black hole collapse. In a generalized Vaidya geometry, the field equations impose a vacuum-like radial pressure; we therefore model the QCD sector phenomenologically by identifying the transverse pressure with the effective QCD pressure. This is neither an isotropic equilibrium treatment nor a first principles simulation of nonequilibrium collapse. Local energy-momentum conservation is used to reconstruct radial temperature, density, and mass profiles for two QCD-inspired equations of state: a finite-chemical-potential chiral model and a finite-density mean-field quark-gluon-plasma model. Although the chiral model admits an exact Lambert-function solution, its physical high-temperature branch has a non-integrable central density. The mean-field model also yields singular temperature and density profiles. Neither produces the cubic near-center mass scaling required for finite curvature. More generally, regularity under the transverse null energy condition uniquely demands a vacuum-like relation between transverse pressure and energy density, which neither QCD closure approaches. Thus, finite quark chemical potential alters the phase-transition thermodynamics but does not generate a self-regularizing core in this framework. Positive-energy mixtures of baryonic matter and radiation also fail to provide the required stress. A smooth matching to an inner de Sitter-like component illustrates the additional short-distance physics needed.

Accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP)