Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions

Abstract

We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdS_{d+1} long wavelength solutions of Einstein's equations with a negative cosmological constant, for all d>2. We find simple explicit expressions for the stress tensor (slightly generalizing the recent result by Haack and Yarom (arXiv:0806.4602)), the full dual bulk metric and an entropy current of this strongly coupled conformal fluid, to second order in the derivative expansion, for arbitrary d>2. We also rewrite the well known exact solutions for rotating black holes in AdS_{d+1} space in a manifestly fluid dynamical form, generalizing earlier work in d=4. To second order in the derivative expansion, this metric agrees with our general construction of the metric dual to fluid flows.

39 pages, 1 figure. JHEP format, v2 : Minor modifications, References added

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Cited by in corpus (10)

• Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries
• Conformal non-relativistic hydrodynamics from gravity
• Gravitational quasinormal modes of AdS black branes in d spacetime dimensions
• Higher Derivative Corrections to Shear Viscosity from Graviton's Effective Coupling
• Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity
• Nonlinear Magnetohydrodynamics from Gravity
• Bifurcation of Plasma Balls and Black Holes to Lobed Configurations
• Second order hydrodynamics for a special class of gravity duals