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75
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.
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
Anomalous transport coefficients from Kubo formulas in Holography
"... Abstract: In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magneti ..."
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Abstract: In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magnetic and vortical conductivities. Whereas a Kubo formula for the anomalous magnetic conductivity is well known we develop a new Kubo type formula that allows the calculation of the vortical conductivity through a two point function of the anomalous current and the momentum density. We also point out that the anomalous vortical conductivity can be understood as a response to a gravitomagnetic field. We apply these Kubo formulas to a simple Holographic system, the Rcharged black hole.
The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm
, 2011
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Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum
, 2014
"... We study the spontaneous parity breaking and generating of Hall viscosity and angular momentum in holographic p+ip model, which can describe stronglycoupled chiral superfluid states in many quantum systems. The dual gravity theory, an SU(2) gauge field minimally coupled to Einstein gravity, is pari ..."
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Cited by 5 (3 self)
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We study the spontaneous parity breaking and generating of Hall viscosity and angular momentum in holographic p+ip model, which can describe stronglycoupled chiral superfluid states in many quantum systems. The dual gravity theory, an SU(2) gauge field minimally coupled to Einstein gravity, is parityinvariant but allows a black hole solution with vector hair corresponding to a paritybroken superfluid state. We show that this state possesses a nonvanishing parityodd transport coefficient – Hall viscosity – and an angular momentum density. We first develop an analytic method to solve this model near the critical regime and to take backreactions into account. Then we solve the equation for the tensor mode fluctuations and obtain the expression for Hall viscosity via Kubo formula. We also show that a nonvanishing angular momentum density can be obtained through the vector mode fluctuations and the corresponding boundary action. We give analytic results of both Hall viscosity and angular momentum density near the critical regime in terms of physical parameters. The nearcritical behavior of Hall viscosity is different from that obtained from a gravitational ChernSimons model. We find that the magnitude of Hall viscosity to angular momentum density ratio is numerically consistent with being equal to 1/2 at large SU(2) coupling corresponding to the probe limit, in agreement with previous results obtained for various quantum fluid systems and from effective theory approaches. In addition, we find the shear viscosity to entropy density ratio remains above the universal bound.
Obers, “Relativistic Elasticity of Stationary Fluid
 Branes,” Phys.Rev. D87 (2013) 044058, arXiv:1210.5197 [hepth
"... Fluid mechanics can be formulated on dynamical surfaces of arbitrary codimension embedded in a background spacetime. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show unde ..."
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Cited by 5 (4 self)
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Fluid mechanics can be formulated on dynamical surfaces of arbitrary codimension embedded in a background spacetime. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of the number of spacetime dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations. ar X iv
How Fluids Bend: the Elastic Expansion for HigherDimensional Black Holes,” arXiv:1304.7773 [hepth
"... Hydrodynamics can be consistently formulated on surfaces of arbitrary codimension in a background spacetime, providing the effective theory describing longwavelength perturbations of black branes. When the codimension is nonzero, the system acquires fluidelastic properties and constitutes what ..."
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Cited by 3 (3 self)
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Hydrodynamics can be consistently formulated on surfaces of arbitrary codimension in a background spacetime, providing the effective theory describing longwavelength perturbations of black branes. When the codimension is nonzero, the system acquires fluidelastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalizes the HelfrichCanham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for codimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For codimension1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)extremal brane effective actions can be accounted for by a multipole expansion of the stressenergy tensor, therefore establishing a relation between the different formalisms of Carter, CapovillaGuven and VasilicVojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.