Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant

Huang, Tai-Zhuo; Ling, Yi; Pan, Weijuan; Tian, Yu; Wu, Xiao-Ning

doi:10.1103/physrevd.85.123531

Cited by 27 publications

(29 citation statements)

References 50 publications

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“…Another instance of the fluid/gravity correspondence in asymptotically flat spacetimes can be found in the blackfold approach [17,18]. Further developments were reported in [19][20][21][22][23][24][25][26][27][28].…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

The relativistic fluid dual to vacuum Einstein gravity

Compère

McFadden

Skenderis

et al. 2012

J. High Energ. Phys.

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We present a construction of a (d + 2)-dimensional Ricci-flat metric corresponding to a (d + 1)-dimensional relativistic fluid, representing holographically the hydrodynamic regime of a (putative) dual theory. We show how to obtain the metric to arbitrarily high order using a relativistic gradient expansion, and explicitly carry out the computation to second order. The fluid has zero energy density in equilibrium, which implies incompressibility at first order in gradients, and its stress tensor (both at and away from equilibrium) satisfies a quadratic constraint, which determines its energy density away from equilibrium. The entire dynamics to second order is encoded in one first order and six second order transport coefficients, which we compute. We classify entropy currents with non-negative divergence at second order in relativistic gradients. We then verify that the entropy current obtained by pulling back to the fluid surface the area form at the null horizon indeed has a non-negative divergence. We show that there are distinct near-horizon scaling limits that are equivalent either to the relativistic gradient expansion we discuss here, or to the non-relativistic expansion associated with the Navier-Stokes equations discussed in previous works. The latter expansion may be recovered from the present relativistic expansion upon taking a specific non-relativistic limit.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

The relativistic fluid dual to vacuum Einstein gravity

Compère

McFadden

Skenderis

et al. 2012

J. High Energ. Phys.

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“…[22][23][24] to a spacetime with a matter field. We have demonstrated that with the help of the Petrov-like condition and Einstein-Maxwell constraints, the incompressible Navier-Stokes equation can be derived for a charged fluid living on the cutoff surface which is embedded into a charged AdS black brane, an RN-AdS black p ðT n n þ 2Ã þ T þ T 00 À 2T 0 n Þ i j À T i…”

Section: Summary and Discussionmentioning

confidence: 99%

“…In Ref. [24], the holographic nature of the Petrov-like condition was further disclosed in a spacetime with a cosmological constant. Based on all the work above, it is reasonable to conjecture that in the approach of fluid/ gravity duality, imposing the Petrov-like condition on the cutoff surface is equivalent to imposing the regularity condition on the future horizon at least in the near-horizon limit.…”

Section: Introductionmentioning

confidence: 98%

Magnetohydrodynamics from gravity

et al. 2012

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Imposing the Petrov-like boundary condition on the hypersurface at finite cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk Einstein equation with electromagnetic field in the near horizon limit. We first get the general framework for spacetime with matter field, and then derive the incompressible Navier-Stokes equations for black holes with electric charge and magnetic charge respectively. Especially, in the magnetic case, the standard magnetohydrodynamic equations will arise due to the existence of the background electromagnetic field on the hypersurface.Comment: 21 page

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“…This cut-off surface approach has been applied in various cases, see [12][13][14]. For example, it was extended for higher curvature gravity theories [15][16][17][18][19] as well as for the AdS [20,21] and dS [22] gravity theories (for other theories, like black branes, see [23]). Very recently, two of the authors of this paper showed in [13] that an incompressible DNS-like equation can be obtained in the cut-off surface approach.…”

Section: Introductionmentioning

confidence: 99%

Effective metric in fluid-gravity duality through parallel transport: A proposal

Dey

Majhi

2019

Phys. Rev. D

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The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods of Riemannian geometry to the study of hydrodynamical flows has been previously explored from a purely mathematical perspective. In this work, we propose a bulk metric in (p+2)-dimensions with the construction being such that the induced metric is flat on a timelike r = r c (constant) slice. We then show that the equations of parallel transport for an appropriately defined bulk velocity vector field along its own direction on this manifold when projected onto the flat timelike hypersurface requires the satisfaction of the incompressible NS equation in (p + 1)-dimensions. Additionally, the incompressibility condition of the fluid arises from a vanishing expansion parameter θ, which is known to govern the convergence (or divergence) of a congruence of arbitrary timelike curves on a given manifold. In this approach Einstein's equations do not play any role and this can be regarded as an off-shell description of fluidgravity correspondence. We argue that our metric effectively encapsulates the information of forcing terms in the governing equations as if a free fluid is parallel transported on this curved background. We finally discuss the implications of this interesting observation and its potentiality in helping us to understand hydrodynamical flows in a probable new setting.

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Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant

Cited by 27 publications

References 50 publications

The relativistic fluid dual to vacuum Einstein gravity

The relativistic fluid dual to vacuum Einstein gravity

Magnetohydrodynamics from gravity

Effective metric in fluid-gravity duality through parallel transport: A proposal

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