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.
Highlights
The AdS/CFT correspondence [1,2,3,4] relates the anti-de Sitter (AdS) space-time to conformal field theory (CFT) on the boundary
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 [43]
At finite temperature and in the long wavelength regime, the dual field theory can be effectively described by fluid mechanics and it can be related to black holes in AdS space-time
Summary
The AdS/CFT correspondence [1,2,3,4] relates the anti-de Sitter (AdS) space-time to conformal field theory (CFT) on the boundary. We consider the fluid/gravity correspondence for Lifshitz geometries and the relation to fluids in boundary non-relativistic theories with Newton-Cartan symmetry. The standard stress-energy tensor we obtain from the holographic calculation is expressed in terms of the fluid variables: velocity field vi, energy density E and pressure P , and contains the (particle number) density n and external source Ai associated to the U(1) symmetry current. It satisfies the condition for Lifshitz invariant theories zE = (d − 1)P.
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