Hyperscaling-Violating Lifshitz hydrodynamics from black-holes: Part II

TL;DR

This paper extends holographic derivations of Lifshitz hydrodynamics to hyperscaling violating theories, revealing non-relativistic behavior with specific viscosity properties and clarifying previous discrepancies in bulk viscosity results.

Contribution

It generalizes Lifshitz hydrodynamics from holography to hyperscaling violating theories with U(1) symmetry, showing new scalar forcing effects and viscosity characteristics.

Findings

Bulk viscosity vanishes in the generalized theory.

Shear viscosity to entropy ratio remains unchanged from relativistic case.

Hydrodynamics aligns with Lifshitz scaling and hyperscaling violation principles.

Abstract

The derivation of Lifshitz-invariant hydrodynamics from holography, presented in [arXiv:1508.02494] is generalized to arbitrary hyperscaling violating Lifshitz scaling theories with an unbroken U(1) symmetry. The hydrodynamics emerging is non-relativistic with scalar "forcing". By a redefinition of the pressure it becomes standard non-relativistic hydrodynamics in the presence of specific chemical potential for the mass current. The hydrodynamics is compatible with the scaling theory of Lifshitz invariance with hyperscaling violation. The bulk viscosity vanishes while the shear viscosity to entropy ratio is the same as in the relativistic case. We also consider the dimensional reduction ansatz for the hydrodynamics and clarify the difference with previous results suggesting a non-vanishing bulk viscosity.