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From NavierStokes to Einstein
, 2011
"... We show by explicit construction that for every solution of the incompressible NavierStokes equation in p + 1 dimensions, there is a uniquely associated “dual ” solution of the vacuum Einstein equations in p + 2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment Σc wh ..."
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We show by explicit construction that for every solution of the incompressible NavierStokes equation in p + 1 dimensions, there is a uniquely associated “dual ” solution of the vacuum Einstein equations in p + 2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment Σc whose extrinsic curvature is given by the stress tensor of the NavierStokes fluid. We consider a “nearhorizon” limit in which Σc becomes highly accelerated. The nearhorizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible NavierStokes equation. For p = 2, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70’s and resurfaced recently in studies of the AdS/CFT correspondence.
Evolving Black Hole Horizons in General Relativity and Alternative Gravity
 GALAXIES
, 2013
"... ..."
Holographic insights and puzzles
"... The talk is composed of two parts, both set within the AdS/CFT context. In the first part, I discuss holographic insight into strongly coupled field theory in a black hole background. I conjecture two new gravitational solutions, dubbed black funnels and black droplets, which describe two distinct d ..."
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The talk is composed of two parts, both set within the AdS/CFT context. In the first part, I discuss holographic insight into strongly coupled field theory in a black hole background. I conjecture two new gravitational solutions, dubbed black funnels and black droplets, which describe two distinct deconfined phases in the field theory at finite temperature. I also briefly mention puzzles associated with an analogous setup in a rotating black hole background. In the second part of the talk, I discuss timedependent states in a CFT on flat spacetime background, exemplified by the conformal soliton flow. Here I focus on puzzles regarding the nature of entropy in timeevolving states and its holographic dual. ar
Black Holes in AdS/BCFT and Fluid/Gravity Correspondence
"... A proposal to describe gravity duals of conformal theories with boundaries (AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However interesting solutions describing field theories at finite temperature and charge density are still lacking. In this paper we describe a class of ..."
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A proposal to describe gravity duals of conformal theories with boundaries (AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However interesting solutions describing field theories at finite temperature and charge density are still lacking. In this paper we describe a class of theories with boundary, which admit black hole type gravity solutions. The theories are specified by stressenergy tensors that reside on the extensions of the boundary to the bulk. From this perspective AdS/BCFT appears analogous to the fluid/gravity correspondence. Among the class of the boundary extensions there is a special (integrable) one, for which the stressenergy tensor is fluidlike. We discuss features of that special solution as well as its thermodynamic properties. ar X iv
CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cutoff surfaces
, 2011
"... We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein’s equations with Dirichlet boundary conditions on fixed timelike cutoff hypersurface. Using the fluid/gravity correspondence, we argu ..."
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We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein’s equations with Dirichlet boundary conditions on fixed timelike cutoff hypersurface. Using the fluid/gravity correspondence, we argue that one can determine nonlinear solutions to this problem in the long wavelength regime. On the boundary we find a conformal fluid with Dirichlet constitutive relations, viz., the fluid propagates on a ‘dynamical ’ background metric which depends on the local fluid velocities and temperature. This boundary fluid can be reexpressed as an emergent hypersurface fluid which is nonconformal but has the same value of the shear viscosity as the boundary fluid. The hypersurface dynamics arises as a collective effect, wherein effects of the background are transmuted into the fluid degrees of freedom. Furthermore, we demonstrate that this collective fluid is forced to be nonrelativistic below a critical cutoff radius in AdS to avoid acausal sound propagation with respect to the hypersurface metric. We further go on to show how one can use this setup to embed the recent constructions of flat spacetime duals to nonrelativistic fluid dynamics into the AdS/CFT correspondence, arguing that a version of the membrane paradigm arises naturally when the boundary fluid lives on a background Galilean manifold.