View of thermodynamic phase transition of the charged Gauss–Bonnet AdS black hole via the shadow

Abstract

We examine thermodynamic phase transition (PT) of the charged Gauss–Bonnet AdS black hole (BH) by utilizing the shadow radius. In this system, we rescale the corresponding Gauss–Bonnet coefficient α by a factor of 1/(D–4), and ensure that α is positive to avoid any singularity problems. The equation derived for the shadow radius indicates that it increases as the event horizon radius increases, making it an independent variable for determining BH temperature. By investigating the PT curve in relation to shadows, we can observe that the shadow radius can be used as an alternative to the event horizon radius in explaining the phenomenon of BH PT. Furthermore, the results indicate that an increase in the parameter α corresponds to a decrease in the temperature of the BH. By utilizing the relationship between the temperature and the shadow radius, it is possible to obtain the thermal profile of the Gauss–Bonnet AdS BH. It is evident that there is an N-type variation in temperature for pressures P < P c. Additionally, as the parameter α increases, the region covered by shadow expands while the temperature decreases. The utilization of BH shadows as a probe holds immense significance in gaining a deeper understanding of BH thermodynamic behavior.