发表机构
New Uzbekistan University; Tashkent State Technical University; University of Tashkent for Applied Sciences; Samarkand State Technical University named after Mirzo Ulugbek; Navoi state university; Institute of Theoretical Physics, National University of Uzbekistan; Kimyo International University in Tashkent; School of Physics, Harbin Institute of Technology（新乌兹别克斯坦大学; 塔什干国立技术大学; 塔什干应用科学大学; 米尔佐·乌鲁格别克撒马尔罕国立技术大学; 纳沃伊国立大学; 乌兹别克斯坦国立大学理论物理研究所; 塔什干化学国际大学; 哈尔滨工业大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过弱非线性展开研究施瓦西分岔附近自发矢量化的爱因斯坦-矢量-高斯-博内黑洞，计算其光子球、阴影等强场修正，发现光子球外移、频率降低等特征。
AI 中文摘要
我们研究了接近其施瓦西分岔的自发矢量化的爱因斯坦-矢量-高斯-博内黑洞的静态、球对称电分支。围绕基本矢量零模构建了弱非线性展开。临界耦合通过打靶法和配置法独立确定，二阶度规修正通过未约化的协变方程进行检验，相应的ADM质量修正被证明解析为零。矢量化分支偏离分岔点的首要项由三阶Fredholm可解性条件给出。利用所得度规，我们计算了光子球、阴影尺度、边际束缚轨道、最内稳定圆轨道、轨道和进动频率、几何三比二频率比半径、圆光子轨道的不稳定性以及对数强偏折系数的主要修正。在分岔附近，光子球和最内稳定轨道向外移动，而三比二半径向内移动。光子轨道角频率降低，其Lyapunov指数增大。这些结果刻画了电矢量化分支的局部强场几何。它们并非旨在作为观测约束或对强非线性区域的推断。
英文摘要
We study the static, spherically symmetric electric branch of spontaneously vectorized Einstein-vector-Gauss-Bonnet black holes close to its Schwarzschild bifurcation. A weakly nonlinear expansion is built around the fundamental vector zero mode. The critical coupling is determined independently by shooting and collocation, the second-order metric correction is checked against the unreduced covariant equations, and the corresponding ADM-mass correction is shown to vanish analytically. The leading departure of the vectorized branch from the bifurcation point follows from a third-order Fredholm solvability condition. Using the resulting metric, we calculate the leading corrections to the photon sphere, shadow scale, marginally bound orbit, innermost stable circular orbit, orbital and epicyclic frequencies, the geometric three-to-two frequency-ratio radius, the instability of the circular photon orbit, and the logarithmic strong-deflection coefficient. Near the bifurcation, the photon sphere and innermost stable orbit move outward, whereas the three-to-two radius moves inward. The photon-orbit angular frequency decreases and its Lyapunov exponent increases. These results characterize the local strong-field geometry of the electric vectorized branch. They are not intended as observational constraints or as an extrapolation to the strongly nonlinear regime.
