Motivated by M-theory/superstring inspired models, we investigate certain behaviors of the deflection angle and shadow geometrical shapes of higher dimensional quintessential black holes associated with two values of the dark energy (DE) state parameter, being \omega=-\frac{1}{3} and \omega=-\frac{2}{3}. Concretely, we derive the geodesic equation of photons on such backgrounds. Thanks to the Gauss-Bonnet theorem associated with the optical metric, we compute the leading terms of the deflection angle in the so-called weak-limit approximation. After that, we inspect the effect of DE and the space-time dimension d on the calculated optical quantities. Introducing DE via the field intensity c and the state parameter \omega, we find that the shadow size and the deflection angle increase by increasing values of the field intensity c. However, we observe that the high dimensions decrease such quantities for \omega-models exhibiting similar behaviors. Then, we consider the effect of the black hole charge, on these optical quantities, by discussing the associated behaviors. The present investigation recovers certain known results appearing in ordinary four dimensional models.

中文翻译：

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任意维度典型黑洞的偏转角和阴影行为

受 M 理论/超弦启发模型的启发，我们研究了与暗能量 (DE) 状态参数的两个值相关的高维典型黑洞的偏转角和阴影几何形状的某些行为，即 \omega=-\frac{ 1}{3} 和 \omega=-\frac{2}{3}。具体来说，我们推导出了这种背景下光子的测地线方程。由于与光学度量相关的 Gauss-Bonnet 定理，我们在所谓的弱极限近似中计算偏转角的主要项。之后，我们检查 DE 和时空维度 d 对计算出的光学量的影响。通过场强 c 和状态参数 ω 引入 DE，我们发现阴影大小和偏转角随着场强 c 的增加而增加。然而，我们观察到，对于表现出类似行为的 omega 模型，高维度会减少这些数量。然后，我们通过讨论相关行为来考虑黑洞电荷对这些光学量的影响。目前的调查恢复了普通四维模型中出现的某些已知结果。