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 a logarithmic nonlinear Yang--Mills field with gauge group SU(2). Unlike solutions based on the Wu--Yang ansatz, the gauge sector contains a dynamical radial amplitude, and the configurations arise from a genuinely coupled nonlinear boundary-value problem. An integral identity excludes nontrivial sign-definite solutions approaching a magnetically neutral Yang--Mills vacuum, implying that colored configurations must be nodal. We numerically construct the fundamental one-node branch and verify its convergence to the ordinary Einstein--Yang--Mills colored black hole in the linear limit. Increasing the logarithmic nonlinearity lowers the ADM mass, raises the Hawking temperature, and displaces the gauge-field node toward larger radii. Branch termination is not detected over the full range of parameters investigated. Instead, the exterior geometry approaches Schwarzschild on fixed radial domains, while the colored structure develops an increasingly extended tail. Although no independent asymptotic Yang--Mills charge is present, the non-Abelian hair leaves a subleading imprint on the far-field geometry. Inside the event horizon, the representative nonlinear solutions possess no Cauchy horizon and approach a Schwarzschild-type spacelike curvature singularity, with a finite limiting mass and no oscillary mass inflation. The recovery of the linear theory is therefore nonuniform near the cetonter: solutions that are nearly linear in the exterior eventually enter the strongly logarithmic regime in the deep interior. Finally, turning points of the Hawking temperature produce divergences and sign changes in heat capacity, indicating transitions of local thermodynamic stability.