Shadow thermodynamics of AdS black hole with the nonlinear electrodynamics term

We creatively employ the shadow radius to study the thermodynamics of a charged Ad S 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 find that the black hole temperature and heat capacity can be presented by the shadow radius.Further analysis shows that the shadow radius can work similarly to the event horizon in revealing black hole phase transition process.In this sense,we construct the thermal profile of the charged Ad S black hole with inclusion of the NLED effect.In the P<Pc case,it is found that the N-type trend of the temperature given by the shadow radius is always consistent with that obtained by using the event horizon.Thus,we can conclude for the charged Ad S black hole that the phase transition process can be intuitively presented as the thermal profile in the shadow context.Finally,the effects of NLED are carefully analyzed.

The shadow and observation appearance of black hole surrounded by the dust field in Rastall theory

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.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,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.