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28
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.
Relativistic viscous hydrodynamics, conformal invariance, and holography
 JHEP
"... Abstract: We consider secondorder viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the secondorder corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bj ..."
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Cited by 85 (2 self)
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Abstract: We consider secondorder viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the secondorder corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) secondorder transport coefficients in the strongly coupled N = 4 supersymmetric YangMills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the MüllerIsraelStewart theory, often used in numerical simulations, does not contain all allowed secondorder terms and, frequently, terms required by conformal invariance. Contents
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
Higher Derivative Corrections to Locally Black Brane Metrics
 JHEP
"... Abstract: In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the GaussBonnet term (with coefficient α ′) as a toy example. We find the solution to the α ′ corrected Einstein equations to first order in the boundary deri ..."
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Cited by 17 (2 self)
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Abstract: In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the GaussBonnet term (with coefficient α ′) as a toy example. We find the solution to the α ′ corrected Einstein equations to first order in the boundary derivative expansion. This allows us to find the α ′ corrections to the boundary stress tensor in the presence of the GaussBonnet term in the bulk action. We therefore obtain the ratio of shear viscosity to entropy which agrees with other methods of computation in the
Forced Fluid Dynamics from Gravity
, 2008
"... We generalise the computations of [1] to generate long wavelength, asymptotically locally AdS5 solutions to the Einsteindilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity, our solutions are dual, under the AdS/CFT correspondenc ..."
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Cited by 16 (1 self)
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We generalise the computations of [1] to generate long wavelength, asymptotically locally AdS5 solutions to the Einsteindilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity, our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parametrised by fourvelocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.
A note on causal hydrodynamics for Mtheory branes,” arXiv:0801.1797 [hepth
"... Abstract: We obtain new transport coefficients of causal hydrodynamics for the M2 and the M5brane using a Kubolike formula proposed by Baier, Romatschke, Son, Starinets, and Stephanov (arXiv:0712.2451 [hepth]). The relaxation times agree with the ones obtained from the “sound mode ” in our paper ..."
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Cited by 11 (0 self)
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Abstract: We obtain new transport coefficients of causal hydrodynamics for the M2 and the M5brane using a Kubolike formula proposed by Baier, Romatschke, Son, Starinets, and Stephanov (arXiv:0712.2451 [hepth]). The relaxation times agree with the ones obtained from the “sound mode ” in our paper (arXiv:0712.2916 [hepth]). Keywords: AdS/CFT correspondence, Brane dynamics in gauge theories. Contents
The dynamics of quarkgluon plasma and AdS/CFT
 Lect. Notes Phys. 828 (2011) 147 [arXiv:1003.3291 [hepth
"... Abstract In these pedagogical lectures, we present the techniques of the AdS/CFT correspondence which can be applied to the study of real time dynamics of a strongly coupled plasma system. These methods are based on solving gravitational Einstein’s equations on the string/gravity side of the AdS/CFT ..."
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Cited by 5 (0 self)
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Abstract In these pedagogical lectures, we present the techniques of the AdS/CFT correspondence which can be applied to the study of real time dynamics of a strongly coupled plasma system. These methods are based on solving gravitational Einstein’s equations on the string/gravity side of the AdS/CFT correspondence. We illustrate these techniques with applications to the boostinvariant expansion of a plasma system. We emphasize the common underlying AdS/CFT description both in the large proper time regime where hydrodynamic dynamics dominates, and in the small proper time regime where the dynamics is far from equilibrium. These AdS/CFT methods provide a fascinating arena interrelating General Relativity phenomenae with strongly coupled gauge theory physics. 1
AdS/CFT applications to relativistic heavy ion collisions: a brief review
 Rept. Prog. Phys. 75 (2012) 124301 [arXiv:1112.5403 [hepph
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