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

TL;DR

This paper investigates the phase transition behavior of dilatonic and conformal Born-Infeld black holes in extended phase space, revealing how parameters influence their thermodynamic criticality and drawing parallels with Van der Waals systems.

Contribution

It introduces a new Lagrangian for dilatonic Born-Infeld theory, derives black hole solutions in Einstein and Jordan frames, and analyzes their $P-V$ criticality through numerical methods.

Findings

Identified critical points and phase transition characteristics of black holes.

Demonstrated the influence of parameters on thermodynamic phase behavior.

Compared thermodynamic properties in Einstein and Jordan frames.

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.