Wilsonian Approach to Fluid/Gravity Duality

Abstract

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty )$ reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant $D(horizon)$ reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $\eta /s$ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.

34 pages, harvmac, clarified boundary condition

References in corpus (9)

• Viscosity, Black Holes, and Quantum Field Theory
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Beyond eta/s = 1/4pi
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Forced Fluid Dynamics from Gravity
• The shear viscosity of gauge theory plasma with chemical potentials
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• Quasinormal spectrum and the black hole membrane paradigm
• Nonlinear Hydrodynamics from Flow of Retarded Green's Function

Cited by in corpus (110)

• Holographic and Wilsonian Renormalization Groups
• Lanczos-Lovelock models of gravity
• From Navier-Stokes To Einstein
• Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm
• The holographic fluid dual to vacuum Einstein gravity
• CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces
• A membrane paradigm at large D
• Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids
• Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
• A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation
• Holographic Schwinger-Keldysh effective field theories
• Non-Relativistic Fluid Dual to Asymptotically AdS Gravity at Finite Cutoff Surface
• The Relativistic Rindler Hydrodynamics
• Conformal Description of Near-Horizon Vacuum States
• Causality and the AdS Dirichlet problem
• Holography of the Photon Ring
• On the stability of gravity with Dirichlet walls
• On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries
• From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime
• Model building in AdS/CMT: DC conductivity and Hall angle
• Hot Halos and Galactic Glasses
• New Massive Gravity and AdS_4 counterterms
• 3D Gravity in a Box
• Incompressible Fluids of the de Sitter Horizon and Beyond
• Holographic Forced Fluid Dynamics in Non-relativistic Limit
• Towards a general fluid/gravity correspondence
• Petrov Classification and holographic reconstruction of spacetime
• Deep learning black hole metrics from shear viscosity
• Holographic Wilsonian RG Flow and Sliding Membrane Paradigm
• Black Holes as Incompressible Fluids on the Sphere
• Magnetohydrodynamics from gravity
• Holographic Entropy Production
• The unconditional RG flow of the relativistic holographic fluid
• Effective hydrodynamics of black D3-branes
• Holographic Screens and Transport Coefficients in the Fluid/Gravity Correspondence
• Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term
• Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant
• Holographic charged fluid dual to third order Lovelock gravity
• Emergent Dark Universe and the Swampland Criteria
• Holographic Charged Fluid with Anomalous Current at Finite Cutoff Surface in Einstein-Maxwell Gravity
• Generating Temperature Flow for eta/s with Higher Derivatives: From Lifshitz to AdS
• Hyperscaling violating black hole solutions and Magneto-thermoelectric DC conductivities in holography
• Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon
• Holographic Interpretation of Acoustic Black Holes
• Counterterms, critical gravity and holography
• Membrane Paradigm and Holographic DC Conductivity for Nonlinear Electrodynamics
• Higher Curvature Gravity and the Holographic fluid dual to flat spacetime
• Mixed RG Flows and Hydrodynamics at Finite Holographic Screen
• Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics
• Holographic Flow of Anomalous Transport Coefficients
• Wilsonian renormalisation and the exact cut-off scale from holographic duality
• Membrane paradigm for Einstein-Gauss-Bonnet gravity
• Novel Features of the Transport Coefficients in Lifshitz Black Branes
• Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT
• Black String Flow
• The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality
• Running Shear Viscosities in Anisotropic Holographic Superfluids
• Petrov type I Condition and Dual Fluid Dynamics
• Holographic Wilsonian flows and emergent fermions in extremal charged black holes
• From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma
• Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
• Holographic RG flow of thermo-electric transports with momentum dissipation
• Petrov type I Spacetime and Dual Relativistic Fluids
• Relativistic Elasticity of Stationary Fluid Branes
• Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity
• Holography as a highly efficient RG flow II: An explicit construction
• Probing the Hydrodynamic Limit of (Super)gravity
• Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity
• The Navier-Stokes equation and solution generating symmetries from holography
• Fluid/gravity correspondence for massive gravity
• Electromagnetic quasinormal modes of rotating black strings and the AdS/CFT correspondence
• Holographic RG flows and transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory
• Holographic fluid from nonminimally coupled scalar-tensor theory of gravity
• Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions
• Bulk Viscosity of dual Fluid at Finite Cutoff Surface via Gravity/Fluid correspondence in Einstein-Maxwell Gravity
• Emergent Dark Matter in Late Time Universe on Holographic Screen
• Wilsonian RG-flow approach to holographic transport with momentum dissipation
• Holographic DC Conductivity for a Power-law Maxwell Field
• Holographic parity violating charged fluid dual to Chern-Simons modified gravity
• Understanding the holographic principle via RG flow
• Connecting the Holographic and Wilsonian Renormalization Groups
• Membrane Paradigm, Gravitational $\Theta$-Term and Gauge/Gravity Duality
• Fluid description of gravity on a timelike cut-off surface: beyond Navier-Stokes equation
• Holographic Complexity for disentangled states
• Dual Fluid for the Kerr Black Hole
• Rindler Fluids from Gravitational Shockwaves
• Quantum Area Fluctuations from Gravitational Phase Space
• Flat space compressible fluid as holographic dual of black hole with curved horizon
• Holographic RG Flow and Sound Modes of sQGP
• Kerr Black string flow
• Linear responses of D0-branes via gauge/gravity correspondence
• Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale
• How Gubser flow ends in a holographic conformal theory
• Deformations of Lifshitz holography with the Gauss-Bonnet term in ($n+1$) dimensions
• Holographic Gubser flow: A combined analytic and numerical study
• Holographic Wilsonian Renormalization and Chiral Phase Transitions
• Effective long distance $q\bar{q}$ potential in holographic RG flows
• Physical Effects of the Gravitational $\Theta$-Parameter
• $U(1)$ current from the AdS/CFT: diffusion, conductivity and causality
• A hydrodynamical description of gravitational waves
• First-Order Viscous Relativistic Hydrodynamics on the Two-Sphere
• Observational Constraints on the Cosmology with Holographic Dark Fluid
• Rindler Fluid with Weak Momentum Relaxation
• Duality and modular symmetry in the quantum Hall effect from Lifshitz holography
• Compressible Fluids in the Membrane Paradigm: non-AdS Fluid/Gravity correspondences
• A note on electrical and thermodynamic properties of Isolated Horizon
• Time evolving fluid from Vaidya spacetime
• Sonic velocity in holographic fluids and its applications
• On the Search for Multicenter AdS Black Holes from M-theory
• RG flow of AC Conductivity in Soft Wall Model of QCD