Critical behavior of Born-Infeld dilaton black holes

Abstract

We explore the critical behavior of (n + 1)-dimensional topological Born-Infeld-dilaton black holes in an extended phase space. We treat the cosmological constant and the Born-Infeld (BI) parameter as the thermodynamic pressure and BI vacuum polarization which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature, Gibbs free energy, and investigate the behaviour of these quantities. We also study the analogy of the van der Waals liquid-gas system with the Born-Infeld-dilaton black holes in canonical ensemble in which we can treat the black hole charge as a fixed external parameter. Moreover, we show that the critical values of pressure, temperature and volume are physical provided the coupling constant of dilaton gravity is less than one and the horizon is sphere. Finally, we calculate the critical exponents and show that although thermodynamic quantities depend on the dilaton coupling constant, BI parameter and the dimension of the spacetime, they are universal and are independent of metric parameters.

Q– $$\Phi $$ Φ criticality in the extended phase space of $$(n+1)$$ ( n + 1 ) -dimensional RN-AdS black holes

“…This traditional method has been extensively applied to the characterization of general thermodynamic systems and also to the establishing of complete simulation for AdS spacetime black hole thermodynamic liquid/gas system [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Heat engines for dilatonic Born–Infeld black holes

“…The thermodynamic volume V is different from the geometrical volume due to the dependence on γ [44],…”

“…For the purpose of computing efficiency, we start from the relevant expression for mass of the Born-Infeld dilaton black hole [44] (details of black hole solutions are reproduced in "Appendix A" for reference),…”

“…Following these works, and the existence of an extended first law with pressure and volume, including the presence of PV criticality allows us to naturally define a heat engine, exactly as in the examples considered for AdS, leading to extension of the results of [30,44,45,68]. The working substance is still the charged black hole, however, the efficiency of heat engines will now depend on the coupling constants provided by dilaton and Born-Infeld theories.…”

“…In particular, we consider the Einstein-Maxwell dilaton system in the presence of two Liouville type potentials and also dilatonic black holes coupled to nonlinear Born-Infeld theory (Dilatonic-BI) in an extended phase space, in fixed charge ensemble [44]. We also consider its conformally consistent counter part, the Brans-Dicke Born-Infeld theory (BD-BI) studied in [45].…”