Generalised Smarr Formula and the Viscosity Bound for Einstein-Maxwell-Dilaton Black Holes

Abstract

We study the shear viscosity to entropy ratio $\eta /S$ in the boundary field theories dual to black hole backgrounds in theories of gravity coupled to a scalar field, and generalisations including a Maxwell field and non-minimal scalar couplings. Motivated by the observation in simple examples that the saturation of the $\eta /S\ge 1/(4\pi )$ bound is correlated with the existence of a generalised Smarr relation for the planar black-hole solutions, we investigate this in detail for the general black-hole solutions in these theories, focusing especially on the cases where the scalar field plays a non-trivial role and gives rise to an additional parameter in the space of solutions. We find that a generalised Smarr relation holds in all cases, and in fact it can be viewed as the bulk gravity dual of the statement of the saturation of the viscosity to entropy bound. We obtain the generalised Smarr relation, whose existence depends upon a scaling symmetry of the planar black-hole solutions, by two different but related methods, one based on integrating the first law of thermodynamics, and the other based on the construction of a conserved Noether charge.

Latex, 36 pages, references added, typos corrected, to appear in PRD

References in corpus (21)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Shear Viscosity from Effective Couplings of Gravitons
• Shear Viscosity from Gauss-Bonnet Gravity with a Dilaton Coupling
• Non-universal shear viscosity from Einstein gravity
• The shear viscosity of gauge theory plasma with chemical potentials
• Thermodynamical First Laws of Black Holes in Quadratically-Extended Gravities
• The shear viscosity of holographic superfluids
• Thermodynamics of Lifshitz Black Holes
• Thermodynamical properties of hairy black holes in n spacetimes dimensions
• The shear viscosity of the non-commutative plasma
• Mass of asymptotically anti-de Sitter hairy spacetimes
• SU(2)-Colored (A)dS Black Holes in Conformal Gravity
• Static and Dynamic Hairy Planar Black Holes
• Thermodynamics of rotating black holes with scalar hair in three dimensions
• A modulated shear to entropy ratio
• Hydrodynamics from scalar black branes
• Hairy black holes in N=2 gauged supergravity
• The Non-integrable Mass and the Scalar Charge

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