Shadow and deflection angle of charged rotating black hole surrounded by perfect fluid dark matter

We analysed the shadow cast by charged rotating black hole (BH) in presence of perfect fluid dark matter (PFDM). We studied the null geodesic equations and obtained the shadow of the charged rotating BH to see the effects of PFDM parameter gamma, charge Q and rotation parameter a, and it is noticed that the size as well as the shape of BH shadow is affected due to PFDM parameter, charge and rotation parameter. Thus, it is seen that the presence of dark matter around a BH affects its spacetime. We also investigated the influence of all the parameters (PFDM parameter gamma, BHs charge Q and rotational parameter a) on effective potential, energy emission by graphical representation, and compare all the results with the non rotating case in usual general relativity. To this end, we have also explored the effect of PFDM on the deflection angle and the size of Einstein rings.

Automated summary

We analyzed the shadow of a charged rotating black hole in the presence of perfect fluid dark matter and found that the size and shape of the shadow are affected by the dark matter parameter, charge, and rotation parameter. Additionally, we investigated the influence of these parameters on effective potential and energy emission, comparing the results to the non-rotating case in general relativity. We also explored the effect of dark matter on the deflection angle and size of Einstein rings.