Extended phase space thermodynamics and P–V criticality: Brans–Dicke–Born–Infeld vs. Einstein–Born–Infeld-dilaton black holes

Abstract

Motivated by a thermodynamic analogy of black holes and Van der Waals liquid/gas systems, in this paper, we study P-V criticality of both dilatonic Born-Infeld black holes and their conformal solutions, Brans-Dicke-BornInfeld solutions. Due to the conformal constraint, we have to neglect the old Lagrangian of dilatonic Born-Infeld theory and its black hole solutions, and introduce a new one. We obtain spherically symmetric nonlinearly charged black hole solutions in both Einstein and Jordan frames and then we calculate the related conserved and thermodynamic quantities. After that, we extend the phase space by considering the proportionality of the cosmological constant and thermodynamical pressure. We obtain critical values of the thermodynamic coordinates through numerical methods and plot the relevant P-V and G-T diagrams. Investigation of the mentioned diagrams helps us to study the thermodynamical phase transition. We also analyze the effects of varying different parameters on the phase transition of black holes.

Heat engines for dilatonic Born–Infeld black holes

“…Computation of corrections to efficiency in the Brans-Dicke Born-Infeld theory proceeds by writing down the relevant expression for enthalpy and equation of state [45] (details of black holes and thermodynamic quantities are summarized in "Appendix B") as …”

“…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]. BD (Brans-Dicke) theory has been significant in the explanation of the cosmic inflation [46], and consistent with Dirac's large number hypothesis and Mach's principle [47,48].…”

“…Also, pressure for asymptotically non-flat/ads black holes with Liouville type potentials has been introduced and the corresponding PV criticality studied in good detail in [68] and extended to conformally coupled scalars, i.e., the BransDicke-Born-Infeld solutions [45]. 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].…”

Phase Transition of Black Holes in Brans–Dicke Born–Infeld Gravity through Geometrical Thermodynamics

“…In this section, we briefly obtain the Einstein-BI-dilaton gravity solutions and then by using the conformal transformation, we calculate the solutions of BD-BI theory [88]. We assume the following metric with various horizon topology:…”