Charge-Hyperscaling Violating Lifshitz hydrodynamics from black-holes

TL;DR

This work demonstrates how Lifshitz-holographic theories with a preserved U(1) symmetry and charge-hyperscaling violation give rise to boundary fluids described by torsional Newton–Cartan geometry. By boosting Lifshitz black holes and applying a derivative expansion, the authors derive a set of non-relativistic fluid equations, identify multiple consistent definitions of the boundary stress-energy tensor, and show how the standard Navier–Stokes dynamics with an external Newton potential emerges in a suitable Newton–Cartan frame. The analysis yields explicit transport coefficients and confirms the KSS-style bound, while revealing a universal structure that persists across Lifshitz exponents, albeit with z- and ψ-dependent constitutive relations. The results illuminate how holographic Lifshitz setups encode non-relativistic hydrodynamics and offer avenues to explore hyperscaling violation, U(1) breaking, and RG flows between relativistic and non-relativistic regimes in strongly coupled systems.

Abstract

Non-equilibrium black hole horizons are considered in scaling theories with generic Lifshitz invariance and an unbroken U(1) symmetry. There is also charge-hyperscaling violation associated with a non-trivial conduction exponent. The boundary stress tensor is computed and renormalized and the associated hydrodynamic equations derived. Upon a non-trivial redefinition of boundary sources associated with the U(1) gauge field, the equations are mapped to the standard non-relativistic hydrodynamics equations coupled to a mass current and an external Newton potential in accordance with the general theory of [arXiv:1502.00228]. The shear viscosity to entropy ratio is the same as in the relativistic case.