In this work, we study the weak gravitational lensing in the background of Kerr-Newman black hole with quintessential dark energy. Initially, we compute the deflection angle of light by charged black hole with quintessential dark energy by utilizing the Gauss-Bnnet theorem. Firstly, we suppose the light rays on the equatorial plane in the axisymmetric spacetime. In doing so, we first find the corresponding optical metrics and then calculate the Gaussian optical curvature to utilize in Gauss-Bonnet theorem. Consequently, we calculate the deflection angle of light for rotating charged black hole with quintessence. Additionally, we also find the deflection angle of light for Kerr-Newman black hole with quintessential dark energy. In order to verify our results, we derive deflection angle by using null geodesic equations which reduces to the deflection angle of Kerr solution with the reduction of specific parameters. Furthermore, we analyze the graphical behavior of deflection angle $\Theta$ w.r.t to impact parameter $b$. Our graphical analysis retrieves various results regarding to the deflection angle by the Kerr-Newman black hole with quintessential dark energy.

中文翻译：

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典型暗能量对克尔-纽曼黑洞弱偏转角的影响

在这项工作中，我们研究了具有典型暗能量的克尔-纽曼黑洞背景中的弱引力透镜效应。最初，我们利用 Gauss-Bnnet 定理计算了具有典型暗能量的带电黑洞的光偏转角。首先，我们假设轴对称时空中赤道面上的光线。为此，我们首先找到相应的光学度量，然后计算高斯光学曲率以在高斯-博内定理中使用。因此，我们用精髓计算了旋转带电黑洞的光偏转角。此外，我们还找到了具有典型暗能量的克尔-纽曼黑洞的光偏转角。为了验证我们的结果，我们通过使用零测地线方程推导出偏转角，该方程随着特定参数的减少而减少到克尔解的偏转角。此外，我们分析了偏转角 $\Theta$ wrt 的图形行为对参数 $b$ 的影响。我们的图形分析检索了有关具有典型暗能量的克尔-纽曼黑洞偏转角的各种结果。