反德西特空间中的带电非阿贝尔黑弦
Electrically Charged Non-Abelian Black String in Anti-de Sitter Space
浏览论文内容
中文总结 AI 辅助
研究在反德西特空间中构造带SU(2)涡旋场的带电非阿贝尔黑弦解，推导其度规形式、非退化界，揭示非阿贝尔毛发的渐近特征，给出数值解实现的非线性形变。
中文摘要 AI 辅助
我们构造了四维爱因斯坦-杨-米尔斯理论的一类新的静态、带电、柱对称黑弦解，该解由真正的非阿贝尔SU(2)涡旋场支撑。电 sector与涡旋 sector的共存使得标准单函数Lemos度规与爱因斯坦方程不相容，需要一个与各向异性杨-米尔斯应力张量兼容的三函数度规。规则的近视界和渐近AdS展开为完整场方程的数值积分提供了边界数据。可恢复两个极限 sector：消失的电视界数据产生零杨-米尔斯场强的中性Lemos黑弦，而关闭涡旋分量则得到嵌入的U(1)⊂SU(2)带电Lemos-Zanchin解。对后者的微扰显示，真正的非阿贝尔毛发在一阶通过对易子场强出现，而其对电分布和几何的反作用在二阶开始。视界方程给出解析的局域非退化界R₁^crit = s₀α√(3/(4πG))。渐近几何呈现可吸收到有效阿贝尔电荷中的二次修正，以及给出非阿贝尔毛发首个不可约渐近特征的三次系数。熵服从贝肯斯坦-霍金面积定律，而与嵌入阿贝尔解的温度差源于渐近 lapse归一化。完全反作用的数值解是该横向非阿贝尔形变的非线性实现。
英文摘要
We construct a new family of static, electrically charged, cylindrically symmetric black-string solutions of four-dimensional Einstein--Yang--Mills theory with a negative cosmological constant, supported by a genuinely non-Abelian $SU(2)$ vortex field. The coexistence of electric and vortex sectors renders the standard single-function Lemos metric inconsistent with the Einstein equations, requiring a three-function metric compatible with the anisotropic Yang--Mills stress tensor. Regular near-horizon and asymptotic AdS expansions provide boundary data for numerical integration of the complete field equations. Two limiting sectors are recovered: vanishing electric horizon datum yields the neutral Lemos black string with zero Yang--Mills field strength, while switching off the vortex component gives the embedded $U(1)\subset SU(2)$ charged Lemos--Zanchin solution. Perturbations about the latter show that genuinely non-Abelian hair appears at linear order through the commutator field strength, whereas its backreaction on the electric profile and geometry begins at quadratic order. The horizon equations yield the analytic local non-degeneracy bound $R_1^{\rm crit}=s_0α\sqrt{3/(4πG)}$. The asymptotic geometry exhibits a quadratic correction absorbable into an effective Abelian charge and a cubic coefficient giving the first irreducible asymptotic signature of the non-Abelian hair. The entropy obeys the Bekenstein--Hawking area law, while the temperature difference from the embedded Abelian solution arises through the asymptotic lapse normalization. The fully backreacted numerical solutions are nonlinear realizations of this transverse non-Abelian deformation.
