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

Abstract

Recently it has been shown that imposing Petrov type I condition on the boundary may reduce the Einstein's equation to the Navier-Stokes equation in the non-relativistic and near-horizon limit. In this paper we extend this framework to a spacetime with a cosmological constant. By explicit construction we show that the Navier-Stokes equation can be derived from both black brane background and spatially curved spacetime. We also conjecture that imposing Petrov type I condition on the boundary should be equivalent to the conventional method using the hydrodynamical expansion of the metric in the near horizon limit.

14 pages; Version published in PRD

References in corpus (15)

• Nonlinear Fluid Dynamics from Gravity
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Forced Fluid Dynamics from Gravity
• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• Non-Relativistic Fluid Dual to Asymptotically AdS Gravity at Finite Cutoff Surface
• From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime
• Incompressible Navier-Stokes Equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell Theories
• From Petrov-Einstein to Navier-Stokes
• Holographic Wilsonian RG Flow and Sliding Membrane Paradigm
• Magnetohydrodynamics from gravity
• Holographic Screens and Transport Coefficients in the Fluid/Gravity Correspondence
• Mixed RG Flows and Hydrodynamics at Finite Holographic Screen

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• Holographic charged fluid dual to third order Lovelock gravity
• Fluid/Gravity Correspondence For General Non-rotating Black Holes
• The Cosmological Constant as a Zero Action Boundary
• The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality
• Petrov type I Condition and Dual Fluid Dynamics
• Petrov type I Spacetime and Dual Relativistic Fluids
• Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
• Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity
• Fluid/gravity correspondence for massive gravity
• Holographic parity violating charged fluid dual to Chern-Simons modified gravity
• Effective metric in fluid-gravity duality through parallel transport: a proposal
• From Petrov-Einstein-Dilaton-Axion to Navier-Stokes equation in anisotropic model
• Fluid description of gravity on a timelike cut-off surface: beyond Navier-Stokes equation
• Gravity dual of Navier-Stokes equation in a rotating frame through parallel transport
• Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence
• A hydrodynamical description of gravitational waves
• Compressible forced viscous fluid from product Einstein manifolds
• Fluids and vortex from constrained fluctuations around C-metric black hole
• Time evolving fluid from Vaidya spacetime