In this paper, we have creatively employed the shadow radius to study the thermodynamics of a charged AdS black hole with a nonlinear electrodynamics(NLED) term. First, the connection between the shadow radius and event horizon is constructed with the aid of the geodesic analysis. It turns out that the black hole shadow radius shows a positive correlation as a function of the event horizon radius. Then in the shadow context, we found that the black hole temperature and heat capacity can be presented by the shadow radius. And further analysis shows that the shadow radius can do as well as the event horizon in revealing black hole phase transition process. In this sense, we constructed the thermal profile of the charged AdS black hole with inclusion of the NLED effect. In P < P c case, it is found that the N -type trend of the temperature given by the shadow radius is always coincide with that obtained by using the event horizon. So, we can concluded for the charged AdS black hole that the phase transition process can be intuitively presented as the thermal profile in the shadow context. Finally, the effects of NLED have been carefully analysed through out the paper.

In this paper, we have creatively employed the shadow radius to study the thermodynamics of a charged AdS black hole with a nonlinear electrodynamics(NLED) term. First, the connection between the shadow radius and event horizon is constructed with the aid of the geodesic analysis. It turns out that the black hole shadow radius shows a positive correlation as a function of the event horizon radius. Then in the shadow context, we found that the black hole temperature and heat capacity can be presented by the shadow radius. And further analysis shows that the shadow radius can do as well as the event horizon in revealing black hole phase transition process. In this sense, we constructed the thermal profile of the charged AdS black hole with inclusion of the NLED effect. In $P<P_c$ case, it is found that the $N$-type trend of the temperature given by the shadow radius is always coincide with that obtained by using the event horizon. So, we can concluded for the charged AdS black hole that the phase transition process can be intuitively presented as the thermal profile in the shadow context. Finally, the effects of NLED have been carefully analysed through out the paper.

In the context of Rastall gravity, the shadow and observation intensity casted by the new Kiselev-like black hole with dust field have been numerically investigated. In this system, the Rastall parameter and surrounding dust field structure parameter have considerable consequences on the geometric structure of spacetime. By considering the photon trajectories near the black hole, we investigate the variation of the radii of photon sphere, event horizon and black hole shadow under the different related parameters. Furthermore, by taking into account two different spherically symmetric accretion models as the only background light source, we also studied the observed luminosity and intensity of black holes. For the both spherical accretions background, the results show that the decrease or increase of the observed luminosity depends on the value range of relevant parameters, and the promotion effect is far less obvious than the attenuation effect on the observed intensity. One can find that the inner shadow region and outer bright region of the black hole wrapped by infalling accretion are significantly darker than those of the static model, which is closely related to the Doppler effect. In addition, the size of the shadow and the position of the photon sphere are always the same in the two accretion models, which means that the black hole shadow depend only on the geometry of spacetime, while the observation luminosity is affected by the form of accretion material and the related spacetime structure.

The study of black hole shadows by considering the surrounding kinds of matter has attracted interest in recent years. In this paper, we use the ray-tracing method to study shadows and photon spheres of renormalization group improved (RGI) black holes, taking into account the different thin spherical accretion models. We find that an increase in the parameters Ω and γ, which are excited by renormalization group theory, can decrease the event horizon and the radius of the photon sphere while increasing the effective potential. For static and infalling accretions, these results indicate that black hole shadows are related to the geometry of spacetime, and are nearly unaffected by spherical accretions. However, due to the Doppler effect, the shadow in the infalling case is darker than the static one, and the intensities of the photon sphere decay more slowly from the photon sphere to infinity. In addition, the peak intensities out of the shadow increase with the parameters Ω and γ. Finally, it can be seen that the effect of Ω on the shadow is more distinct by comparing it with that of γ at the same parameter level.

In this paper, we study the shadows and observational appearance of the Ayón-Beato-García (ABG) black hole, which is surrounded by a thin disk accretion. For a four-dimensional ABG black hole, as the charge q increases, the event horizon $r_+$, radius $r_{p}$ and impact parameter $b_p$ of the photon sphere decrease, while the maximum value of effective potential $V_{eff}$ increases. However, as the term $\gamma$ associated with nonlinear electrodynamics increases, the related physical quantities $r_+$, $r_p$ and $b_p$ increase, but the maximum value of $V_{eff}$ decreases. When the light ray reaches the vicinity of the ABG black hole, one can observe the trajectories of the light rays appear as three types, i.e., direct emission, lens ring and photon ring. Furthermore, the shadows and the observational appearance of the ABG black hole are studied. The results show that the charge $q$ and the term $\gamma$ have a great influence on the shape and intensity of the black hole shadow. When the relevant state parameters change or the emission model changes, it can be argued that it is the direct emission that plays a decisive role in the total observed intensity of the ABG black hole, while the contribution of the lens ring to the total observed intensity is small and the photon ring makes almost no contribution.