Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

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. At first, 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 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 they depend on dilaton coupling constant as well as 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 case of $T>T_c$, we have no phase transition. When $T=T_c$, the system admits a second order phase transition, while for $T=T_{\rm f}<T_c$ the system experiences a first order transition. Interestingly, for $T_{\rm f}<T<T_c$ we observe a \textit{zeroth order} phase transition in the presence of dilaton field. This novel \textit{zeroth order} phase transition is occurred due to a finite jump in Gibbs free energy which is generated by dilaton-electromagnetic coupling constant, $\alpha$, for a certain range of pressure.

Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field

Taking the Noether gauge symmetry approach into account, we find spherically symmetric static black hole solutions of the non-minimal gauge-gravity Lagrangian of the $\mathcal{R}^\beta F^2$ model. At first, we consider a system of differential equations for the general non-minimal couplings of $Y(\mathcal{R})F^2$ type, and then, we regard a particular $\mathcal{R}^\beta F^2$ non-minimal model to find the exact black hole solution and analyze its symmetries. As the next step, we calculate the thermodynamical quantities of the black hole and study its interesting behavior. Besides, we address thermal stability and examine the possibility of the van der Waals-like phase transition.Comment: 17 pages, 20 figure

Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity

We investigate a new class of $(n+1)$-dimensional topological black hole solutions in the context of massive gravity and in the presence of logarithmic nonlinear electrodynamics. Exploring higher dimensional solutions in massive gravity coupled to nonlinear electrodynamics is motivated by holographic hypothesis as well as string theory. We first construct exact solutions of the field equations and then explore the behavior of the metric functions for different values of the model parameters. We observe that our black holes admit the multi-horizons caused by a quantum effect called anti-evaporation. Next, by calculating the conserved and thermodynamic quantities, we obtain a generalized Smarr formula. We find that the first law of black holes thermodynamics is satisfied on the black hole horizon. We study thermal stability of the obtained solutions in both canonical and grand canonical ensembles. We reveal that depending on the model parameters, our solutions exhibit a rich variety of phase structures. Finally, we explore, for the first time without extending thermodynamics phase space, the critical behavior and reentrant phase transition for black hole solutions in massive gravity theory. We realize that there is a zeroth order phase transition for a specified range of charge value and the system experiences a large/small/large reentrant phase transition due to the presence of nonlinear electrodynamics.Comment: 14 pages (one column), 12 captioned figure

Thermodynamic stability of a new three dimensional regular black hole

A new model of the regular black hole in $(2+1)-$dimensions is introduced by considering an appropriate matter field as the energy-momentum tensor. First, we propose a novel model of $d$-dimensional energy density that in $(2+1)-$dimensions leads to the existence of an upper bound on the radius of the event horizon and a lower bound on the mass of the black hole which are motivated by the features of astrophysical black holes. According to these bounds, we introduce an admissible domain for the event horizon radius, depending on the metric parameters. After investigation of geometric properties of the obtained solutions, we study the thermal stability of the solution in the canonical ensemble and find that the regular black hole is thermally stable in the mentioned admissible domain. Besides, the Gibbs free energy is calculated to examine the global stability of the solution.Comment: 21 pages, 14 figures, 2 tables, Comments are welcom