Shadow thermodynamics of AdS black hole in regular spacetime

TL;DR

This paper explores the relationship between black hole shadows and thermodynamics in regular spacetime, demonstrating how shadow radius can serve as a probe for phase transitions and thermal properties of Bardeen-AdS black holes.

Contribution

It establishes a novel connection between black hole shadow radius and thermodynamic phase transitions in regular spacetime, enabling shadow-based analysis of black hole thermodynamics.

Findings

Shadow radius correlates positively with event horizon radius.

Shadow radius can replace event horizon radius in phase transition analysis.

Thermal profile exhibits N-type behavior in certain conditions.

Abstract

The dependence of the black hole (BH) shadow and thermodynamics may be structured in the regular spacetime. Taking the regular Bardeen-AdS BH as an example, the relationship between the shadow radius and the 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 the regular spacetime. By analyzing the phase transition curves under the shadow context, we found 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 the phase structure in the regular spacetime. Utilizing the temperature-shadow radius function, the thermal profile of the Bardeen-AdS BH is established. We obtained that the temperature shows an N-type change trend in P<Pc situation. These results suggest that the phase transition process of the 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 the regular spacetime.