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85
Nonlinear Fluid Dynamics from Gravity
, 2007
"... Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields – arbitrary functions of the coordinates on the boundary of AdS5 – we use Einstein’s equations together with regularity requ ..."
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Cited by 122 (4 self)
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Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields – arbitrary functions of the coordinates on the boundary of AdS5 – we use Einstein’s equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.
Fluid dynamics of Rcharged black holes
"... We construct electrically charged AdS5 black hole solutions whose charge, mass and boostparameters vary slowly with the spacetime coordinates. From the perspective of the dual theory, these are equivalent to hydrodynamic configurations with varying chemical potential, temperature and velocity fiel ..."
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Cited by 75 (3 self)
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We construct electrically charged AdS5 black hole solutions whose charge, mass and boostparameters vary slowly with the spacetime coordinates. From the perspective of the dual theory, these are equivalent to hydrodynamic configurations with varying chemical potential, temperature and velocity fields. We compute the boundary theory transport coefficients associated with a derivative expansion of the energy momentum tensor and Rcharge current up to second order. In particular, we find a first order transport coefficient
Gravity & Hydrodynamics: Lectures on the fluidgravity correspondence
, 2009
"... We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluidgravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in ..."
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Cited by 73 (1 self)
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We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluidgravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in the strongly interacting boundary field theory. We explain how the geometric duals to the fluid dynamics are constructed in a boundary derivative expansion and use the construction to extract the hydrodynamic transport coefficients. In addition we also describe the recent developments extending the correspondence to incorporate matter fields and to nonrelativistic systems. Based on
Universal hydrodynamics of nonconformal branes
"... We examine the hydrodynamic limit of nonconformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to nonconformal brane solutions by showing that all such solutions can be obtained from high ..."
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Cited by 54 (5 self)
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We examine the hydrodynamic limit of nonconformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to nonconformal brane solutions by showing that all such solutions can be obtained from higher dimensional asymptotically locally AdS solutions by suitable dimensional reduction and continuation in the dimension. As a consequence, many holographic results for such backgrounds follow from the corresponding results of the Asymptotically AdS case. In particular, the hydrodynamics of nonconformal branes is fully determined in terms of conformal hydrodynamics. Using previous results on the latter we predict the form of the nonconformal hydrodynamic stress tensor to second order in derivatives. Furthermore we show that the ratio between bulk and shear viscosity is fixed by the generalized conformal structure to be ζ/η = 2(1/(d − 1) − c2 s), where cs is the speed The AdS/CFT correspondence provides a powerful tool to study strongly coupled quantum field theories. In particular, it has become possible to explore strongly coupled finite temperature
Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT
, 2008
"... We compute coefficients of twoderivative terms in the hydrodynamic energy momentum tensor of a viscous fluid which has an AdSD dual with 3 ≤ D ≤ 7. For the case of D = 3 we obtain an exact AdS3 black hole solution, valid to all orders in a derivative expansion, dual to a perfect fluid in 1 + 1 dime ..."
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Cited by 41 (3 self)
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We compute coefficients of twoderivative terms in the hydrodynamic energy momentum tensor of a viscous fluid which has an AdSD dual with 3 ≤ D ≤ 7. For the case of D = 3 we obtain an exact AdS3 black hole solution, valid to all orders in a derivative expansion, dual to a perfect fluid in 1 + 1 dimensions.
The Holographic fluid dual to vacuum Einstein gravity, [arXiv:1103.3022 [hepth
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Relativistic Viscous Fluid Dynamics and NonEquilibrium Entropy
, 906
"... Abstract: Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains the most general (causal) equations of motion for a ..."
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Cited by 33 (2 self)
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Abstract: Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains the most general (causal) equations of motion for a fluid in the presence of shear and bulk viscosity, as well as the structure of the nonequilibrium entropy current. Requiring positivity of the divergence of the nonequilibrium entropy current relates some of its coefficients to those entering the equations of motion. I comment on possible