Thanks for the releasing image of supermassive black holes (BHs) by the event horizon telescope (EHT) at the heart of the M87 galaxy. After the discovery of this mysterious object, scientists paid attention to exploring the BH shadow features under different gravitational backgrounds. In this scenario, we study the light rings and observational properties of BH shadow surrounded by different accretion flow models and then investigate the effect of model parameters on the observational display and space-time structure of BHs in the framework of our considering system. Under the incompatible configuration of the emission profiles, the images of BHs comprise that the observed luminosity is mainly determined by direct emission, while the lensing ring will provide a small contribution of the total observed flux and the photon ring makes a negligible contribution due to its exponential narrowness. More importantly, the observed regions and specific intensities of all emission profiles are changed correspondingly under variations of parameters. For optically thin accreting matters, we analyze the profile and specific intensity of the shadows with static and infalling accretions models, respectively. We find that with an infalling motion the interior region of the shadows will be darker than the static case, due to the Doppler effect of the infalling movement. Finally, it is concluded that these findings support the fact that the change of BH state parameters will change the way of space-time geometry, thus affecting the BH shadow dynamics.

Here we provide shadow images of a Kerr-like black hole (BH) in cold dark matter (CDM) halo illuminated with a celestial light source and a thin accretion disk. The impact of spin parameter a, critical density ρ_c and the scale radius R_s on the observed images of BHs is carefully addressed. The results indicate that as a increases, the circular orbits are shifted rightwards, while the larger values of both ρ_c and R_s are the cause to enhance the radius of circular orbits of the BH shadow. In the case of the celestial light source, the impact of ρ_c on shadow distortion is negligible, but this influence is relatively smaller and becomes appreciable when the parameter R_s has larger values. Next, we discuss the intensity and the size of the inner shadow, which are gradually increasing with the increase of both ρ_c and R_s . On the other hand, in the case of retrograde flow, the intensity of the shadow images significantly decreases, and a crescent moon emerges on the upper right side of the screen. Subsequently, the distinctive features of red-shift factors for direct and lensed images with prograde and retrograde flows are discussed. The outcomes indicate that the distribution of red-shift factors and the optical appearance are closely related to the behaviour of accreting flow as well as with relevant parameters. Using the recent observational data of EHT, we found that the shadow's angular diameter of Sgr A* provides the best-fit parameter constraints as compared to M87*.

The light passing near the black hole (BH) is deflected due to the gravitational effect, producing the BH shadow, a dark inner region that is often surrounded by a bright ring, whose optical appearance comes directly from BH’s mass and its angular momentum. We mainly study the shadow and observable features of non-commutative (NC) charged Kiselev BH, surrounded by various profiles of accretions. To obtain the BH shadow profile, we choose specific values of the model parameters and concluded that the variations of each parameter directly vary the light trajectories and size of BH. For thin disk accretion, which includes direct lensing and photon rings emissions, we analyze that the profile of BH contains the dark interior region and bright photon ring. However, their details depends upon the emissions, generally, direct emission plays significant role in the total observed luminosity, while lensing ring has a small contribution and the photon ring makes a negligible contribution, as usual, the latter can be ignored safely. Moreover, we also consider the static and infalling accretion matters and found that the location of the photon sphere is almost the same for both cases. However, the specific intensity which is observed from BH profile found to be darker for infalling accretion case due to the Doppler effect of the infalling motion as compared to the static one.

In the context of holography, the Einstein ring of an AdS black hole (BH) in massive gravity (MG) is depicted. An oscillating Gaussian source on one side of the AdS boundary propagates in bulk, and we impose a response function to explain it. Using a wave optics imaging system, we obtain the optical appearance of the Einstein ring. Our research reveals that the ring can change into a luminosity-deformed ring or light spots depending on the variation of parameters and observational positions. When observers are positioned at the north pole, the holographic profiles always appear as a ring with concentric stripe surroundings, and a bright ring appears at the location of the photon sphere of the BH. To investigate the distinct features of the MG AdS BH from previous studies, we discussed the relation between the temperature T and the event horizon u_e , which shows the decaying behavior with the increasing values of the event horizon u_e , when the graviton parameter m is fixed. These in turn influence the behavior of the response function and the Einstein ring. For example, the amplitude of the lensed response function |〈O〉| increases with the increasing values of the graviton parameter m, for the fixed value of the horizon u_e . On the other hand, the amplitude of the lensed response function |〈O〉| decreases with the increasing values of the horizon u_e , for the fixed value of graviton parameter m. These differences are also reflected in the Einstein ring, where the intensities and the locations of the Einstein ring significantly vary according to the numerical values of the involved parameters. These findings are also observed in the brightness profiles and the best fit comparison between the results obtained by wave optics and geometric optics for different values of graviton parameter m. In this perspective, our study contributes to a better understanding of the analytical studies of holographic theory, which can be used to evaluate different types of BHs for a fixed wave source and optical system.

In this paper, we mainly study the shadow and observable features of a dyonic black hole (DBH) with a global monopole surrounded by perfect fluid under various profiles of accretions. We investigate the influence of model parameters on the observational signatures and space-time structure of black holes (BHs). We observe that the value of $$b_{ps}$$b ps increases with the increasing values of $$\alpha $$α and $$\eta $$η , while it decreases with the increasing values of the electromagnetic parameter. We found that the corresponding regions and the observed specific intensities of the direct, lensing and photon ring emissions dramatically changed according to the variation of BH state parameters. It is noticed that the total observed flux is dominated by the direct emission and the lensing ring makes a small contribution while the photon ring makes a negligible contribution due to its exponential narrowness, even the photon ring intersects the thin plane more than three times to pick up a larger intensity. Assuming the spherically symmetric accretion disk, it is found that due to the Doppler effect of infalling motion, shadows of infalling accretion are found to be darker as compared to static ones. However, the size and position of the DBH shadows do not change in both cases, implying that the BH’s shadow size depends on the geometric space-time and the shadow’s luminosities rely on the accretion flow models. Finally, the discussion is done analytically and numerically, and ray-tracing methods are adopted to obtain the proper visualizations.