Ehrenfest's scheme and thermodynamic geometry in Born-Infeld AdS black holes

In this paper, we analyze the phase transition phenomena in Born-Infeld anti-de Sitter (BI AdS) black holes using Ehrenfest's scheme of standard thermodynamics. The critical points are marked by the divergences in the heat capacity. In order to investigate the nature of the phase transition, we analytically check both Ehrenfest equations near the critical points. Our analysis reveals that this is indeed a second order phase transition. Finally, we analyze the nature of the phase transition using the state space geometry approach. This is found to be compatible with Ehrenfest's scheme.