Abstract
In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. First of all, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with the Van der Waals liquid–gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show that they depend on the dilaton coupling constant as well as on the nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in the case of T>T_c, we have no phase transition. When T=T_c, the system admits a second-order phase transition, while for T=T_mathrm{f}<T_c the system experiences a first-order transition. Interestingly, for T_mathrm{f}<T<T_c we observe a zeroth-order phase transition in the presence of a dilaton field. This novel zeroth-order phase transition occurs due to a finite jump in the Gibbs free energy which is generated by the dilaton–electromagnetic coupling constant, alpha , for a certain range of pressure.
Highlights
Nowadays, it is a general belief that there should be some deep connection between gravity and thermodynamics.Bekenstein [1,2] was the first who disclosed that a black hole can be regarded as a thermodynamic system with entropy and temperature proportional, respectively, to the horizon area and surface gravity [1,2,3,4]
When the gauge field is in the form of logarithmic and exponential nonlinear electrodynamics, critical behavior of black hole solutions in Einstein gravity has been explored [15]
In the context of Born–Infeld and power-Maxwell nonlinear electrodynamics coupled to the dilaton field, critical behavior of (n + 1)-dimensional topological black holes in an extended phase space has been explored in [46,47], respectively
Summary
It is a general belief that there should be some deep connection between gravity and thermodynamics. When the gauge field is in the form of logarithmic and exponential nonlinear electrodynamics, critical behavior of black hole solutions in Einstein gravity has been explored [15]. In the context of Born–Infeld and power-Maxwell nonlinear electrodynamics coupled to the dilaton field, critical behavior of (n + 1)-dimensional topological black holes in an extended phase space has been explored in [46,47], respectively. We will see that in addition to the firstand second-order phase transition in charged black holes, the presence of the dilaton field admits a zeroth-order phase transition in the system This phase transition is occurred due to a finite jump in the Gibbs free energy which is generated by dilaton–electromagnetic coupling constant, α, for a certain range of pressure.
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