Lifshitz hydrodynamics at generic $z$ from a moving black brane

TL;DR

This paper develops a holographic model of Lifshitz hydrodynamics for non-equilibrium steady states in quantum critical fluids with arbitrary dynamical exponent z, using moving black branes in Einstein-Maxwell-Dilaton gravity.

Contribution

It introduces a holographic framework for Lifshitz hydrodynamics at generic z, including non-zero momentum, extending previous models to non-relativistic, scale-invariant fluids.

Findings

Derived the non-relativistic stress tensor complex holographically.

Established the thermodynamics of Lifshitz black branes with generic z.

Provided a concrete realization of Lifshitz perfect fluid dynamics.

Abstract

A Lifshitz black brane at generic dynamical critical exponent $z > 1$, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz perfect fluid with a generic dynamical critical exponent.