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Lifshitz hydrodynamics from Lifshitz black branes with linear momentum

par Hartong, Jelle ;Obers, Niels N.A.;Sanchioni, Marco
Référence The Journal of high energy physics, 2016, 10, 120
Publication Publié, 2016-10

Article révisé par les pairs

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Résumé :

We construct a new class of 4-dimensional z = 2 Lifshitz black branes that have a non-zero linear momentum. These are solutions of an Einstein-Proca-dilaton model that can be obtained by Scherk-Schwarz circle reduction of AdS5 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 Schrödinger perfect fluid with broken particle number symmetry.