Abstract:
Born-Infeld AdS black hole exhibits a reentrant phase transition for certain values of the Born-Infeld
parameter b. This behavior is an additional feature compared to the van der Waals like phase transition
observed in charged AdS black holes. Therefore, it is worth observing the underlying microscopic origin of
this reentrant phase transition. Depending on the value of the parameter b, the black hole system has four
different cases: no phase transition, a reentrant phase transition with two scenarios, or a van der Waals-like
(standard) phase transition. In this article, by employing a novel Ruppeiner geometry method in the
parameter space of temperature and volume, we investigate the microstructure of Born-Infeld AdS black
hole via the phase transition study, which includes standard and reentrant phase transitions. We find that the
microstructures of the black hole that lead to standard and reentrant phase transitions are distinct in nature.
The standard phase transition is characterized by the typical RN-AdS microstructure. In this case, the small
black hole phase has a dominant repulsive interaction for the low temperature case. Interestingly, during the
reentrant phase transition, displayed by the system in a range of pressures for specific b values, the
dominant attractive nature of interaction in the microstructure is preserved. Our results suggest that in the
reentrant phase transition case, the intermediate black holes behave like a bosonic gas, and in the standard
phase transition case the small black holes behave like a quantum anyon gas. In both cases, the large black
hole phase displays an interaction similar to the bosonic gas. The critical phenomenon is observed from the
curvature scalar, including the signature of the reentrant phase transition
