Reentrant phase transition of Born-Infeld-AdS black holes

Abstract

We investigate thermodynamic phase structure and critical behaviour of Born-Infeld (BI) black holes in an anti-de Sitter (AdS) space, where the charge of the system can vary and the cosmological constant (pressure) is fixed. We find that the BI parameter crucially affects the temperature of the black hole when the horizon radius, r+, is small. We observe that depending on the value of the nonlinear parameter, β, BI-AdS black hole may be identified as RN black hole for Q ≥ Qm, and Schwarzschild-like black hole for Q < Qm, where Qm = 1/ (8πβ) is the marginal charge. We analytically calculate the critical point (Qc, Tc, r+c) by solving the cubic equation and study the critical behaviour of the system. We also explore the behavior of Gibbs free energy for BI-AdS black hole. We find out that the phase behaviour of BI-AdS black hole depends on the charge Q. For Q > Qc, the Gibbs free energy is single valued and the system is locally stable (CQ > 0), while for Q < Qc, it becomes multivalued and CQ < 0. In the range of Qz < Q < Qc, a first order phase transition occurs between small black hole (SBH) and large black hole (LBH). Interestingly enough, in the range of Qt ≤ Q ≤ Qz, a reentrant phase transition occurs between intermediate (large) black hole, SBH and LBH in Schwarzschild-type region. This means that in addition to the first order phase transition which separates SBH and LBH, a finite jump in Gibbs free energy leads to a zeroth order phase transition between SBH and intermediate black hole (LBH) where initiates from Q = Qz and terminates at Q = Qt.

Thermodynamics and phase transition of a nonlinear electrodynamics black hole in a cavity

“…Using asymptotically AdS boundary conditions, the thermodynamics of BI black holes was considered in [63][64][65]. For the RN type in Regions I and II, the phase structure of a BI black hole in a cavity is analogous to that of the corresponding BI-AdS black hole.…”

“…The thermodynamic behavior and phase transitions of BI black holes in various gravities were investigated in [50][51][52][53][54][55][56][57][58][59][60][61][62]. Especially, the thermodynamics of a 4D BI-AdS black hole was studied in [63][64][65], where a reentrant phase transition was always observed in a certain region of the parameter space.…”

Fractional-order phase transition of charged AdS black holes

“…In the extended phase space, one can construct a one-to-one correspondence between the thermodynamic quantities of AdS black hole and those of ordinary thermodynamic systems [21]. After that, many other AdS black holes and other interesting critical phenomena have been extensively explored [22][23][24][25][26][27][28][29][30][31][32].…”

Universality class of alternative phase space and Van der Waals criticality

“…All these phase transitions are also discussed from the thermogemetrical point of view [17] where the phase transition is identified as the divergence of the Ricci scalar of the thermodynamic geometry. In additional, an interesting phenomenon of black hole reentrant phase transition has also been investigated in fourdimensional Born-Infeld AdS black in which the charge of system can vary and the cosmological constant is fixed [18].…”