AI 中文总结
该研究在爱因斯坦引力与SU(2)对数非线性杨-米尔斯场耦合框架下，构造静态球对称有色黑洞，数值分析其特性并揭示热力学稳定性转变。
AI 中文摘要
我们在四维爱因斯坦引力与具有规范群SU(2)的对数非线性杨-米尔斯场耦合的框架中，构造了静态、球对称且渐近平直的有色黑洞。与基于Wu-Yang假设的解不同，规范部分包含一个动力学径向振幅，该构型源自一个真正耦合的非线性边值问题。一个积分恒等式排除了趋近于磁中性杨-米尔斯真空的非平凡符号定解，意味着有色构型必须是节点型的。我们数值构造了基态单节点分支，并验证其在线性极限下收敛于普通爱因斯坦-杨-米尔斯有色黑洞。增大对数非线性强度会降低ADM质量、提高霍金温度，并使规范场节点向更大半径移动。在所研究的全部参数范围内未检测到分支终止；相反，外几何在固定径向域上趋近于施瓦西几何，而有色结构形成越来越延展的尾迹。尽管不存在独立的渐近杨-米尔斯荷，非阿贝尔毛发仍在远场几何中留下次主导印记。在事件视界内部，代表性非线性解无柯西视界，趋近于施瓦西型类空曲率奇点，具有有限极限质量且无振荡质量暴胀。因此，线性理论在中心附近的恢复是不均匀的：外部近线性的解最终在深内部进入强对数 regime。最后，霍金温度的转折点会导致热容出现发散和符号变化，表明局部热力学稳定性发生转变。
英文摘要
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.
Comments24 pages, 5 figures
