Abstract
Motivated by thermodynamic analogy of black holes and Van der Waals liquid/gas system, in this paper, we study $P-V$ criticality of both dilatonic Born-Infeld black holes and their conformal solutions, Brans-Dicke-Born-Infeld 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 thermodynamic coordinates through numerical methods and plot relevant $P-V$ and $G-T$ diagrams. Investigation of the mentioned diagrams helps us to study thermodynamical phase transition. We also analyze the effects of varying different parameters on the phase transition of black holes.
Highlights
In 1872 James Clerk Maxwell combined the electricity and magnetism laws in a unified theory
We should note that the characteristic swallow-tail behavior in G–T diagrams guarantees the existence of the phase transition
The main goal was studying the properties of BD-BI black hole solutions
Summary
In 1872 James Clerk Maxwell combined the electricity and magnetism laws in a unified theory. Thermodynamical properties of higher dimensional charged rotating black brane solutions in BDBI gravity are presented in Ref. Regarding gauge/gravity duality, nonlinearly charged black holes with a non-minimal coupling to a scalar field are good candidates for the gravitational side as regards duality to Lifshitz-like theories [46,52,53]. Regarding black hole thermodynamics as an important connection between quantum gravity and the classical nature of general relativity [54], one may be motivated to consider thermal phase transitions. The thermodynamic behavior of charged black hole solutions in BD theory and the analogy of these solutions with the Van der Waals liquid– gas system in the extended phase space was investigated in Ref. We study the P–V criticality and phase transition of charged black holes in BD-BI theory and compare it with Einstein–BI-dilaton solutions. We discuss P–V criticality of the black holes in both Einstein and Jordan frames
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