In this paper, we construct the slowly rotating case of an asymptotically flat supermassive black hole embedded in dark matter using Newman–Janis procedure. Our analysis is carried with respect to the involved parameters including the halo total mass M and the galaxy’s lengthscale \(a_0\). Concretly, we investigate the dark matter impact on the effective potential and the photon sphere. In particular, we find that the lengthscale \(a_0\) controles such potential values. Indeed, for low \(a_0\) values, we find that the halo total mass M decreases the potential values significantly while for high \(a_0\) values such impact is diluted. Regarding the shadow aspects, we show that the shadow size is much smaller for high values of \(a_0\) while the opposite effect is observed when the halo total mass M is increased. By comparing our case to the slowly rotating case, we notice that the former exhibits a shadow shifted from its center to the left side. Finally, we compute the deflection angle in the weak-limit approximation and inspect the dark matter parameters influence. By ploting such quantity, we observe that one should expect lower bending angle values for black holes in galactic nuclei.

在本文中，我们使用纽曼-贾尼斯程序构建了嵌入暗物质的渐近平坦超大质量黑洞的缓慢旋转情况。我们的分析是针对涉及的参数进行的，包括晕总质量M和星系的长度尺度\(a_0\)。具体来说，我们研究了暗物质对有效势和光子球的影响。特别是，我们发现长度尺度\(a_0\)控制着这样的潜在值。事实上，对于低\(a_0\)值，我们发现光环总质量M显着降低了潜在值，而对于高\(a_0\)值，这种影响被稀释。关于阴影方面，我们表明，对于较高的\(a_0\)值，阴影尺寸要小得多，而当光晕总质量M增加时，会观察到相反的效果。通过将我们的案例与缓慢旋转的案例进行比较，我们注意到前者的阴影从其中心转移到左侧。最后，我们计算弱极限近似中的偏转角并检查暗物质参数的影响。通过绘制这样的量，我们观察到，星系核中的黑洞的弯曲角值应该较低。