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.
Future Roadmap:
Introduction
In this paper, we examine the slowly rotating case of a supermassive black hole embedded in dark matter. We investigate the impact of dark matter on the effective potential, the photon sphere, and the shadow size. We also analyze the deflection angle in the weak-limit approximation and discuss the influence of dark matter parameters.
Impact of Dark Matter on Effective Potential
We first focus on the effect of dark matter on the effective potential. The lengthscale (a0) of the galaxy controls the potential values. For low a0 values, increasing the halo total mass (M) leads to a significant decrease in potential values. However, for high a0 values, this impact is diluted. Further analysis is required to understand the underlying mechanisms behind these observations.
Photon Sphere and Shadow Size
We then shift our attention to the photon sphere and its relationship with dark matter. We find that the size of the shadow is much smaller for high values of a0. On the other hand, increasing the halo total mass (M) results in a larger shadow size. These findings suggest that the interplay between galaxy lengthscale and dark matter can lead to variations in the observed shadow characteristics.
Comparison with Slowly Rotating Case
To gain further insights, we compare our case with the slowly rotating case. Interestingly, we observe that the former exhibits a shadow shifted from its center to the left side. This discrepancy could be due to the influence of dark matter on the overall spacetime curvature near the black hole. Further investigations are needed to fully understand this phenomenon.
Influence of Dark Matter Parameters and Deflection Angle
Finally, we examine the influence of dark matter parameters on the deflection angle in the weak-limit approximation. By plotting this quantity, we observe that black holes in galactic nuclei are expected to have lower bending angle values. This suggests that the presence of dark matter affects the path of light passing near the black hole. Understanding this influence can provide valuable insights into galaxy dynamics and the role of dark matter in shaping the Universe.
Conclusion
In conclusion, our analysis highlights the intricate relationship between supermassive black holes, dark matter, and various astrophysical phenomena. The impact of dark matter on the effective potential, photon sphere, shadow size, and deflection angle warrants further investigation. By unraveling these complex interactions, we can deepen our understanding of the Universe, its constituents, and the fundamental laws that govern it.