Shadow thermodynamics of an AdS black hole in regular spacetime * *Supported by the National Natural Science Foundation of China (11903025)

Abstract

The dependence of the black hole (BH) shadow and thermodynamics may be structured in regular spacetime. Taking a regular Bardeen-AdS BH as an example, the relationship between the shadow radius and event horizon radius is derived. It is found that these two radii display a positive correlation, implying that the BH temperature can be rewritten as a function of shadow radius in regular spacetime. By analyzing the phase transition curves under the shadow context, we find that the shadow radius can replace the event horizon radius to present the BH phase transition process, and the phase transition grade can also be revealed by the shadow radius, indicating that the shadow radius may serve as a probe for phase structure in regular spacetime. Utilizing the temperature-shadow radius function, the thermal profile of the Bardeen-AdS BH is established. Moreover, the temperature exhibits an N-type change trend in the situation. These results suggest that the phase transition process of a regular AdS BH can be completely presented in the thermal profile, and the relationship between the BH shadow and thermodynamics can also be established in regular spacetime.