Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum

TL;DR

This paper constructs a new class of Lifshitz black branes with linear momentum, revealing a novel Lifshitz hydrodynamics on Newton-Cartan space-time with unique thermodynamic properties.

Contribution

It introduces Lifshitz black branes with nonzero linear momentum and develops the associated Lifshitz hydrodynamics framework on Newton-Cartan geometry.

Findings

Black branes with linear momentum are constructed.

A new Lifshitz hydrodynamics formulation is derived.

Linear momentum acts as a chemical potential in the fluid.

Abstract

We construct a new class of 4-dimensional z=2 Lifshitz black branes that have a nonzero linear momentum. These are solutions of an Einstein-Proca-dilaton model that can be obtained by Scherk-Schwarz circle reduction of AdS_5 gravity coupled to a free real scalar field. The boundary of a bulk Lifshitz space-time is a Newton-Cartan geometry. We show that the fluid dual to the moving Lifshitz black brane leads to a novel form of Lifshitz hydrodynamics on a Newton-Cartan space-time. Since the linear momentum of the black brane cannot be obtained by a boost transformation the velocity of the fluid or rather, by boundary rotational invariance, its magnitude plays the role of a chemical potential. The conjugate dual variable is mass density. The Lifshitz perfect fluid can be thought of as arising from a Schroedinger perfect fluid with broken particle number symmetry.