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

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.

31 pages, 16 figures (some figures include two subfigures). V2: some typos corrected, some references added

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Cited by in corpus (13)

• Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics
• Charged scalar quasi-normal modes for linearly charged dilaton-Lifshitz solutions
• Thermodynamics of dyonic black holes with Thurston horizon geometries
• One-dimensional backreacting holographic superconductors with exponential nonlinear electrodynamics
• Slowly rotating Einstein-Maxwell-dilaton black hole and some aspects of its thermodynamics
• The Lifshitz black branes and DC transport coefficients in massive Einstein-Maxwell-dilaton gravity
• Duality family of scalar field
• Holographic insulator/superconductor transition with exponential nonlinear electrodynamics probed by entanglement entropy
• Self-energy problem, vacuum polarization, and dual symmetry in Born-Infeld-type $U(1)$ gauge theories
• Entropy of higher-dimensional topological dS black holes with nonlinear source
• Optical properties of Born-Infeld-dilaton-Lifshitz holographic superconductors
• On double-black hole solutions of the Einstein-Maxwell-Dilaton theory in five dimensions
• Thermodynamic geometric analysis of RN black holes under f(R) gravity