AI 中文总结
本文研究Kalb-Ramond引力中双荷黑洞的弱强引力透镜，推导偏转角与透镜方程，并利用Sgr A*和M87*观测给出电荷约束，构建观测量以分离有效电荷与锥形参数。
AI 中文摘要
我们研究了Kalb-Ramond引力中双荷黑洞的弱场和强场引力透镜效应。在固定渐近归一化后，我们区分了控制局部零测地线轨迹的有效电荷与与洛伦兹对称性破缺相关的全局角向识别。在弱偏折区域，我们显式计算了高斯曲率，并应用带有扰动光线边界的Gauss-Bonnet定理，恢复了完整的二阶质量贡献。基于轨道方程、转折点积分和费马原理的独立计算重现了相同的偏转角。在强偏折区域，Tsukamoto方法给出了两个强偏折系数的闭合表达式，具有精确的电荷依赖性。我们推导了有限距离透镜方程以及相关的图像位置、放大率、通量比和微分到达时间，并保留了物理缠绕条件。从Sgr A$^*$和M87$^*$的观测推断出的阴影尺寸给出了条件性电荷界限，并辅以S2进动的估计。我们进一步构建了强透镜观测量的组合，以在模型内将有效电荷与锥形参数分离：角间距和相对亮度消除了显式的缠绕依赖性，而结合独立距离估计的时间比则隔离了锥形形变。
英文摘要
We investigate the weak and strong gravitational lensing of a dyonic black hole in Kalb-Ramond gravity. After fixing the asymptotic normalization, we distinguish the effective charge governing the local null trajectories from the global angular identification associated with Lorentz-symmetry breaking. In the weak-deflection regime, we evaluate the Gaussian curvature explicitly and apply the Gauss-Bonnet theorem with a perturbed ray boundary, recovering the complete second order mass contribution. Independent calculations based on the orbit equation, the turning point integral, and Fermat's principle reproduce the same bending angle. In the strong-deflection regime, Tsukamoto's method yields closed expressions for both strong-deflection coefficients, with exact charge dependence. We derive finite-distance lens equations and the associated image positions, magnifications, flux ratios, and differential arrival times, retaining the physical winding condition. Shadow sizes inferred from observations of Sgr~A$^*$ and M87$^*$ yield conditional charge bounds, complemented by an estimate from S2 precession. We further construct combinations of strong-lensing observables that separate the effective charge from the conical parameter within the model: angular separation and relative brightness remove the explicit winding dependence, while a timing ratio incorporating an independent distance estimate isolates the conical deformation.
Comments44 pages, 3 figures and 5 tables. Suggestions/Comments (about contents and refs) are welcome
