Microscopic origin of black hole reentrant phase transitions

Abstract

Understanding the microscopic behavior of the black holes ingredients has been one of the important challenges in black holes physics during the past decades. In order to shed some light on the microscopic structure of black holes, in this paper, we explore a recently observed phenomenon for black holes namely reentrant phase transition, by employing the Ruppeiner geometry. Interestingly enough, we observe two properties for the phase behaviour of small black holes that leads to reentrant phase transition. They are correlated and they are of the interaction type. For the range of pressure in which the system underlies reentrant phase transition, it transits from large black holes phase to small one which possesses higher correlation than the other ranges of pressures. On the other hand, the type of interaction between small black holes near large/small transition line, differs for usual and reentrant phase transitions. Indeed, for usual case, the dominant interaction is repulsive whereas for reentrant case we encounter with an attractive interaction. We show that in reentrant phase transition case, the small black holes behave like a Bosonic gas whereas in the usual phase transition case, they behave like a quantum anyon gas.