Revisiting the Born–Infeld-AdS black hole phase structure through Landau theory and free energy landscape approaches
Abstract
In our present work, we probe the thermal phase transition structure, the dynamic and kinetic behavior of the Born–Infeld-AdS black hole. With the emergence of a triple point behavior and the possible ruling out the reentrant phase transition, for a certain parametric value of the charge parameter, we scrutinize the stochastic dynamics and the kinetic processes using the free energy landscape formalism. Such processes occur during the black hole phase transitions in terms of the Landau functional and equivalently by the Fokker–Planck equation in the context of black hole chemistry. Our analysis establishes a pertinent bridge between the thermal behavior among the different states of the Van-der-Waals-like fluids and the Born–Infeld-AdS black hole phases. To visualize the direct implications of the Landau functional of the usual Van-der-Waals-like fluids, we consistently employed the generic Landau formalism. We find that such investigations are worthy of study in implementing the continuous phase transition behavior during Hawking radiation. For more details, and in addition to the exploitation of the Landau functional, we introduce its convexity to determine its extreme points and the corresponding stable and unstable phases of the thermal black hole systems. We systematically study the behavior of the first-order and the second-order phase transitions and look into details of their evolution during thermal transitions. Moreover, knowing that the thermal phase transitions…
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