AI 中文总结
该研究在爱因斯坦-矢量-高斯-邦尼理论中构造分析静态多极黑洞，得到电、磁扇区的不同分支解，明确其分岔特性与多极矩的分离规律，丰富了黑洞解的相关研究。
AI 中文摘要
我们在具有二次耦合函数的爱因斯坦-矢量-高斯-邦尼理论中构造并分析了静态多极黑洞。矢量化解在高斯-邦尼耦合的离散值处从史瓦西黑洞分岔而来，这些离散值通过史瓦西背景上的微扰本征值问题得到，并由角多极数ℓ标记。我们限制在基频径向分支上。电扇区包含已知的球对称ℓ=0分支以及ℓ>0的轴对称分支，这些电分支延伸至更大的耦合值。磁扇区具有一系列轴对称分支，包括先前发现的ℓ=0的磁偶极分支，而磁分支仅存在于耦合的有限区间内，终止于临界解。在分岔点之外，非线性效应会产生额外的多极矩，但偶ℓ和奇ℓ矩仍保持分离。
英文摘要
We construct and analyze static multipolar black holes in Einstein-vector-Gauss-Bonnet theory with a quadratic coupling function. The vectorized solutions bifurcate from the Schwarzschild black hole at discrete values of the Gauss-Bonnet coupling, obtained from a perturbative eigenvalue problem on the Schwarzschild background and labelled by the angular multipole number $\ell$. We restrict to the fundamental radial branches. The electric sector contains the known spherically symmetric $\ell=0$ branch as well as axisymmetric branches with $\ell>0$. These electric branches extend to larger values of the coupling. The magnetic sector features a sequence of axisymmetric branches, including the previously found magnetic dipole branch at $\ell=0$. The magnetic branches instead exist only on finite intervals of the coupling, ending at critical solutions. Away from the bifurcation point, nonlinearities generate additional multipoles, but even-$\ell$ and odd-$\ell$ moments remain separated.
Comments15 pages, 4 figures
