Thermodynamics and gauge/gravity duality for Lifshitz black holes in the presence of exponential electrodynamics

TL;DR

This paper constructs Lifshitz black hole solutions with exponential electrodynamics, analyzes their thermodynamics and stability, and explores holographic properties like conductivity and shear viscosity ratio, revealing effects of nonlinearity and Lifshitz scaling.

Contribution

It introduces new Lifshitz black hole solutions with nonlinear exponential electrodynamics and studies their thermodynamics, stability, and holographic transport properties.

Findings

Thermodynamics obeys the first law and a Smarr formula.

Holographic conductivity vanishes for $z>3$ with nonlinear electrodynamics.

Numerical results match experimental data for conductivity behaviors.

Abstract

In this paper, we construct a new class of topological black hole Lifshitz solutions in the presence of nonlinear exponential electrodynamics for Einstein-dilaton gravity. We show that the reality of Lifshitz supporting Maxwell matter fields exclude the negative horizon curvature solutions except for the asymptotic AdS case. Calculating the conserved and thermodynamical quantities, we obtain a Smarr type formula for the mass and confirm that thermodynamics first law is satisfied on the black hole horizon. Afterward, we study the thermal stability of our solutions and figure out the effects of different parameters on the stability of solutions under thermal perturbations. Next, we apply the gauge/gravity duality in order to calculate the ratio of shear viscosity to entropy for a three-dimensional hydrodynamic system by using the pole method. Furthermore, we study the behavior of holographic conductivity for two-dimensional systems such as graphene. We consider linear Maxwell and nonlinear exponential electrodynamics separately and disclose the effect of nonlinearity on holographic conductivity. We indicate that holographic conductivity vanishes for $z>3$ in the case of nonlinear electrodynamics while it does not in the linear Maxwell case. Finally, we solve perturbative additional field equations numerically and plot the behaviors of real and imaginary parts of conductivity for asymptotic AdS and Lifshitz cases. We present experimental results match with our numerical ones.