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Hyperscaling-violating Lifshitz hydrodynamics from black-holes. II. (English) Zbl 1377.83048

Summary: For part I see [J. High Energy Phys. 2015, No. 12, Paper No. 076, 51 p. (2015; doi:10.1007/JHEP12(2015)076)].
The derivation of Lifshitz-invariant hydrodynamics from holography, presented in part I 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.

MSC:

83C57 Black holes
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
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