Abstract
We explore a novel reentrant phase transition of four-dimensional Born–Infeld-dilaton black hole in which the first order phase transition modify into a zeroth order phase transition below the critical point. Working in the extended phase space with regarding the cosmological constant as a pressure, we study the reentrant behavior of phase transition in the canonical ensemble. We show that these black holes enjoy a zeroth order intermediate-small black hole phase transition as well as a first order phase transition between small and large black holes for a narrow range of temperatures and pressures. We also find that the standard first order small–large black hole phase transition can modify into a zeroth order type. This zeroth order phase transition stands between the critical point and the first order phase transition region. We discuss the significant effect of the scalar field (dilaton) on the mentioned interesting treatment.
Highlights
P = − 8π, (1)where the thermodynamical quantity conjugate to P is the thermodynamical volume ∂M V= ∂P, rep (2)in which “r ep” stands for “residual extensive parameters”
The cosmological constant stands by pressure side in Tolman–Oppenheimer– Volkoff equation which shows the cosmological constant can be considered as thermodynamical pressure
Considering as the pressure of system leads to a van der Waals like small– large black holes (SBH–LBH) phase transition which has been investigated by so many authors
Summary
In which “r ep” stands for “residual extensive parameters”. The motivation comes from the fact that in some fundamental theories there are several physical constants, such as Yukawa coupling, gauge coupling constants, and Newton’s constant that are not fixed values. In our black holes case study, there is a specific range of temperatures such that black holes undergo a large–small–large phase transition by a monotonic changing of the pressure. This interesting phenomenon has been first observed in a nicotine–water mixture [24], and seen in multicomponent fluids, binary gases, liquid crystals, and other diverse systems [25]. The van der Waals like phase transition of SBH– LBH in dilaton gravity has been investigated for charged adS black holes [33], and different types of nonlinear electrodynamics, such as power Maxwell invariant [34,35], exponential [36], and Born–Infeld [37,38]. The electric potential U , measured at infinity with respect to the horizon is given by the following explicit form
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