From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime

Abstract

We generalize the framework in arXiv:1104.5502 to the case that an embedding may have a nonvanishing intrinsic curvature. Directly employing the Brown-York stress tensor as the fundamental variables, we study the effect of finite perturbations of the extrinsic curvature while keeping the intrinsic metric fixed. We show that imposing a Petrov type I condition on the hypersurface geometry may reduce to the incompressible Navier-Stokes equation for a fluid moving in spatially curved spacetime in the near-horizon limit.

17 pages, references added, generalizing the metric form in part 3, version published in JHEP

References in corpus (6)

• The Incompressible Non-Relativistic Navier-Stokes Equation 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
• Incompressible Navier-Stokes Equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell Theories
• Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant

Cited by in corpus (31)

• The relativistic fluid dual to vacuum Einstein gravity
• Incompressible Navier-Stokes Equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell Theories
• Towards a general fluid/gravity correspondence
• Holographic Forced Fluid Dynamics in Non-relativistic Limit
• Magnetohydrodynamics from gravity
• Holographic charged fluid dual to third order Lovelock gravity
• Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant
• Holographic Charged Fluid with Anomalous Current at Finite Cutoff Surface in Einstein-Maxwell Gravity
• Fluid/Gravity Correspondence For General Non-rotating Black Holes
• Novel Features of the Transport Coefficients in Lifshitz Black Branes
• The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality
• Petrov type I Condition and Dual Fluid Dynamics
• Gravity-mediated holography in 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
• The Navier-Stokes equation and solution generating symmetries from holography
• Fluid/gravity correspondence for massive gravity
• Bulk Viscosity of dual Fluid at Finite Cutoff Surface via Gravity/Fluid correspondence in Einstein-Maxwell Gravity
• On the Magnetohydrodynamics/Gravity Correspondence
• Effective metric in fluid-gravity duality through parallel transport: a proposal
• Holographic parity violating charged fluid dual to Chern-Simons modified gravity
• 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
• Flat space compressible fluid as holographic dual of black hole with curved horizon
• Rindler Fluid with Weak Momentum Relaxation
• Compressible forced viscous fluid from product Einstein manifolds
• Fluids and vortex from constrained fluctuations around C-metric black hole
• Sonic velocity in holographic fluids and its applications
• Incompressible Stars and Fractional Derivatives
• Time evolving fluid from Vaidya spacetime