Critical behavior of Born-Infeld dilaton black holes

TL;DR

This paper investigates the phase transition and critical phenomena of Born-Infeld-dilaton black holes in higher dimensions, revealing universal critical exponents despite parameter dependencies.

Contribution

It introduces a detailed thermodynamic analysis of Born-Infeld-dilaton black holes, including critical behavior and universality of critical exponents in extended phase space.

Findings

Critical values are physical for coupling constant < 1 and spherical horizon.

Thermodynamic quantities exhibit van der Waals-like behavior.

Critical exponents are universal, independent of metric parameters.

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 xponents and show that although thermodynamic quantities depend on the dilaton oupling constant, BI parameter and the dimension of the spacetime, they are universal and are independent of metric parameters.