Local Fluid Dynamical Entropy from Gravity

Abstract

Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed.

Latex, 30 pages + 20 pages appendices. 3 eps figures. v2: typos corrected

References in corpus (20)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Nonlinear Fluid Dynamics from Gravity
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Viscosity Bound and Causality Violation
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Near-horizon symmetries of extremal black holes
• Entropy Current in Conformal Hydrodynamics
• Viscous plasma evolution from gravity using AdS/CFT
• Viscous hydrodynamics relaxation time from AdS/CFT
• The stress-energy tensor of a quark moving through a strongly-coupled N=4 supersymmetric Yang-Mills plasma: comparing hydrodynamics and AdS/CFT
• The shear viscosity of gauge theory plasma with chemical potentials
• Shear viscosity of boost invariant plasma at finite coupling
• On the supergravity description of boost invariant conformal plasma at strong coupling
• Elliptic Flow, Kasner Universe and Holographic Dual of RHIC Fireball
• Plasmarings as dual black rings
• Gravity dual of 1+1 dimensional Bjorken expansion
• Spherically expanding matter in AdS/CFT
• A note on causal hydrodynamics for M-theory branes
• The magnetohydrodynamics model of twin kilohertz QPOs in LMXBs

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• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
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• Gravity Dual of a Quantum Hall Plateau Transition
• Extremal vacuum black holes in higher dimensions
• Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
• Conformal non-relativistic hydrodynamics from gravity
• Quasinormal spectrum and the black hole membrane paradigm
• Consistent holographic description of boost-invariant plasma
• Gravitational quasinormal modes of AdS black branes in d spacetime dimensions
• CFT Hydrodynamics: Symmetries, Exact Solutions and Gravity
• Nonlinear Magnetohydrodynamics from Gravity
• Bifurcation of Plasma Balls and Black Holes to Lobed Configurations
• Thermodynamics of Plasmaballs and Plasmarings in 3+1 Dimensions
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• Hydrodynamic Flow of the Quark-Gluon Plasma and Gauge/Gravity Correspondence
• The fluid/gravity correspondence: Lectures notes from the 2008 Summer School on Particles, Fields, and Strings