Effective Lifshitz black holes, hydrodynamics, and transport coefficients in fluid/gravity correspondence

TL;DR

This paper explores Lifshitz black holes within the fluid/gravity framework, calculating transport coefficients like conductivity and viscosity, and analyzing their implications for dual Lifshitz field theories.

Contribution

It introduces effective Lifshitz black holes with arbitrary dynamical exponents and computes key transport and response coefficients in the dual field theory.

Findings

Calculated charge diffusion constant and shear mode damping constant.

Determined shear-viscosity-to-entropy density ratio.

Obtained electrical DC conductivity via holographic linear response.

Abstract

Effective Lifshitz black holes with arbitrary dynamical exponent are addressed in the fluid/gravity membrane paradigm. The transport and the response coefficients in the dual Lifshitz field theory are calculated and analyzed, including the charge diffusion constant and the shear mode damping constant, along with the shear-viscosity-to-entropy density ratio. The Kubo formula is employed to obtain the electrical DC conductivity for the gauge sector corresponding to impurity through the holographic linear response of gauge vector fluctuations in the Lifshitz black brane geometry.