Colored black holes in logarithmic nonlinear Yang–Mills theory

Abstract

We construct static, spherically symmetric, and asymptotically flat colored black holes in four-dimensional Einstein gravity coupled to logarithmic nonlinear Yang–Mills theory with gauge group SU(2). Unlike exact solutions based on the Wu–Yang ansatz, these configurations contain a dynamical radial gauge amplitude and arise from a fully coupled boundary-value problem. An integral identity establishes that nontrivial magnetically neutral solutions must be nodal. We obtain the fundamental one-node branch and verify its smooth convergence to the ordinary Einstein–Yang–Mills colored black hole in the weakly nonlinear regime. Increasing the logarithmic nonlinearity lowers the ADM mass, raises the Hawking temperature, and shifts the gauge-field node outward. No termination of the branch is detected within the parameter and radial ranges investigated; instead, the exterior geometry approaches Schwarzschild on fixed radial domains while the colored field develops an increasingly extended tail. A characteristic analysis shows that sufficiently strong logarithmic deformations lose hyperbolicity near the event horizon, restricting their dynamical interpretation. Although the non-Abelian hair carries no independent asymptotic charge, it leaves a subleading gravitational imprint. For representative solutions within the investigated parameter and radial ranges, the numerical interior evolution detects neither an inner Cauchy horizon nor oscillatory mass inflation. Their mass function approaches a finite limit, while the center remains a Schwarzschild-type spacelike curvature singularity. The recovery of the linear theory is nonuniform near the center, where every finite nonlinear deformation eventually enters the strongly logarithmic regime. Temperature turning points also mark changes of local thermodynamic stability, without implying a global phase transition.