Petrov type I Condition and Dual Fluid Dynamics

Abstract

Recently Lysov and Strominger [arXiv:1104.5502] showed that imposing Petrov type I condition on a $(p+1)$-dimensional timelike hypersurface embedded in a $(p+2)$-dimensional vacuum Einstein gravity reduces the degrees of freedom in the extrinsic curvature of the hypersurface to that of a fluid on the hypersurface, and that the leading-order Einstein constraint equations in terms of the mean curvature of the embedding give the incompressible Navier-Stokes equations of the dual fluid. In this paper we show that the non-relativistic fluid dual to vacuum Einstein gravity does not satisfy the Petrov type I condition at next order, unless additional constraint such as the irrotational condition is added. In addition, we show that this procedure can be inversed to derive the non-relativistic hydrodynamics with higher order corrections through imposing the Petrov type I condition, and that some second order transport coefficients can be extracted, but the dual "Petrov type I fluid" does not match the dual fluid constructed from the geometry of vacuum Einstein gravity in the non-relativistic limit. We discuss the procedure both on the finite cutoff surface via the non-relativistic hydrodynamic expansion and on the highly accelerated surface via the near horizon expansion.

20 pages, published version, with minor improvements

References in corpus (14)

• Nonlinear Fluid Dynamics from Gravity
• Classification of the Weyl Tensor in Higher Dimensions and Applications
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• A generalized Damour-Navier-Stokes equation applied to trapping horizons
• Non-Relativistic Fluid Dual to Asymptotically AdS Gravity at Finite Cutoff Surface
• AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
• From Petrov-Einstein to Navier-Stokes
• Magnetohydrodynamics from gravity
• Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term
• Holographic charged fluid dual to third order Lovelock gravity
• Higher Curvature Gravity and the Holographic fluid dual to flat spacetime
• The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality
• Petrov type I Spacetime and Dual Relativistic Fluids

Cited by in corpus (12)

• Towards a general fluid/gravity correspondence
• Fluid/Gravity Correspondence For General Non-rotating Black Holes
• The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality
• Petrov type I Spacetime and Dual Relativistic Fluids
• Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity
• Fluid/gravity correspondence for massive gravity
• Holographic fluid from nonminimally coupled scalar-tensor theory of gravity
• Emergent Dark Matter in Late Time Universe on Holographic Screen
• Holographic parity violating charged fluid dual to Chern-Simons modified gravity
• Rindler Fluid with Weak Momentum Relaxation
• Observational Constraints on the Cosmology with Holographic Dark Fluid
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction