# Shadow Thermodynamics of AdS Black Hole with the Nonlinear Electrodynamics Term

## TL;DR

This paper explores how the shadow radius of a charged AdS black hole with nonlinear electrodynamics can be used to analyze its thermodynamics and phase transitions, providing a new perspective beyond traditional horizon-based methods.

## Contribution

It introduces a novel approach linking black hole shadow radius to thermodynamic properties and phase transitions in charged AdS black holes with NLED effects.

## Key findings

- Shadow radius correlates positively with event horizon radius.
- Shadow radius can reveal black hole phase transitions.
- Temperature profiles from shadow analysis match traditional methods.

## Abstract

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 < Pc 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.