Thermodynamics, photon sphere and thermodynamic geometry of Ayón-Beato–García Space–time

We study the thermodynamics of the Ayón-Beato–García black hole and the relationship between photon orbits and the thermodynamic phase transitions of the black hole in AdS space–time. We then examine the interactions between the microstructures of the black hole using Ruppeiner geometry. The radius of the photon orbit and the minimum impact parameter behave nonmonotonically below the critical point, mimicking the behavior of Hawking temperature and pressure in extended thermodynamics. Their changes during the large black hole–small black hole phase transition serve as the order parameter, possessing a critical exponent of [Formula: see text]. The results demonstrate that the gravity and thermodynamics of the Ayón-Beato–García black hole are closely related. Furthermore, we explore the thermodynamic geometry, which provides insight into the microstructure interactions of the black hole. We find that the large black hole phase is analogous to a bosonic gas with a dominant attractive interaction, while the small black hole phase behaves like an anyonic gas with both attractive and repulsive interactions.