Shear Viscosity to Entropy Density Ratio in Higher Derivative Gravity with Momentum Dissipation

Abstract

We investigate $\eta /s$ in linear scalar fields modified Gauss-Bonnet theory that breaks translation invariance. We first calculate $\eta /s$ both analytically and numerically and show its relationship with temperature in log-log plot. Our results show that $\eta /s\sim T^2$ at low temperatures. The causality is also considered in this work. We then find that causality violation still happens in the presence of the linear scalar field and we suggest there is a Gauss-Bonnet coupling dependent lower limit for the effective mass of the graviton. If the effective mass of the graviton is big enough, then there will be no causality violation and hence no constraints for the Gauss-Bonnet coupling.

arXiv comment21 pages, 5 figures, revised version, references added, to appear in PRD

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• Holographic Studies of The Generic Massless Cubic Gravities
• Universality of DC Electrical Conductivity from Holography
• Holographic RG flow of thermo-electric transports with momentum dissipation
• Violation of the viscosity/entropy bound in translationally invariant non-Fermi liquids
• Black holes in 4D Einstein-Maxwell-Gauss-Bonnet gravity coupled with scalar fields
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• Hysteresis in $\eta /s$ for QFTs dual to spherical black holes
• Sound modes and stability of momentum dissipated black branes in holography
• Shear viscoelasticity in anisotropic holographic axion model