An Action for and Hydrodynamics from the improved Large D membrane

Abstract

It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einstein's equations. The equation of motion of this membrane is determined by the membrane stress tensor. In this paper we `improve' the membrane stress tensor derived in earlier work to ensure that it defines consistent probe membrane dynamics even at finite $D$ while reducing to previous results at large D. Our improved stress tensor is the sum of a Brown York term and a fluid energy momentum tensor. The fluid has an unusual equation of state; its pressure is nontrivial but its energy density vanishes. We demonstrate that all stationary solutions of our membrane equations are produced by the extremisation of an action functional of the membrane shape. Our action is an offshell generalization of the membrane's thermodynamical partition function. We demonstrate that the thermodynamics of static spherical membranes in flat space and global AdS space exactly reproduces the thermodynamics of the dual Schwarzschild black holes even at finite D. We study the long wavelength dynamics of membranes in AdS space, and demonstrate that the boundary `shadow' of this membrane dynamics is boundary hydrodynamics with with a definite constitutive relation. We determine the explicit form of shadow dual boundary stress tensor upto second order in derivatives of the boundary temperature and velocity, and verify that this stress tensor agrees exactly with the fluid gravity stress tensor to first order in derivatives, but deviates from the later at second order and finite D.

arXiv comment64 pages, v2: footnote added, some typos corrected

References in corpus (72)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Nonlinear Fluid Dynamics from Gravity
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Constraints on Fluid Dynamics from Equilibrium Partition Functions
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Essentials of Blackfold Dynamics
• The large D limit of General Relativity
• World-Volume Effective Theory for Higher-Dimensional Black Holes
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Adiabatic hydrodynamics: The eightfold way to dissipation
• Schwinger-Keldysh formalism I: BRST symmetries and superspace
• Large D gravity and low D strings
• Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT
• Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current
• Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography
• On the hydrodynamic attractor of Yang-Mills plasma
• Large rotating AdS black holes from fluid mechanics
• Effective theory of Black Holes in the 1/D expansion
• Evolution and endpoint of the black string instability: Large D solution
• The Fluid Manifesto: Emergent symmetries, hydrodynamics, and black holes
• Dissipative superfluid dynamics from gravity
• Resurgence in Extended Hydrodynamics
• Hydrodynamics, resurgence and trans-asymptotics
• CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces
• Black Holes as Lumps of Fluid
• Effective actions for anomalous hydrodynamics
• Decoupling and non-decoupling dynamics of large D black holes
• A membrane paradigm at large D
• The eightfold way to dissipation
• Universal quasinormal modes of large D black holes
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• Hydro-elastic Complementarity in Black Branes at large D
• Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions
• Schwinger-Keldysh formalism II: Thermal equivariant cohomology
• Instability of rotating black holes: large D analysis
• Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions
• Derivation of the blackfold effective theory
• The holographic dual of a Riemann problem in a large number of dimensions
• Entropy Current from Partition Function: One Example
• Entropy current and equilibrium partition function in fluid dynamics
• Off-shell hydrodynamics from holography
• Non-uniform black strings and the critical dimension in the $1/D$ expansion
• The large D black hole Membrane Paradigm at first subleading order
• How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
• Currents and Radiation from the large $D$ Black Hole Membrane
• The second law of thermodynamics from symmetry and unitarity
• Plasmarings as dual black rings
• Quasinormal modes of Gauss-Bonnet black holes at large D
• Instability of de Sitter Reissner-Nordstrom black hole in the 1/D expansion
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Black rings at large D
• Unstable `black branes' from scaled membranes at large $D$
• Holographic superconductivity in the large D expansion
• On Brane Instabilities in the Large $D$ Limit
• Holographic Turbulence in a Large Number of Dimensions
• Forced Fluid Dynamics from Blackfolds in General Supergravity Backgrounds
• Static Gauss-Bonnet Black Holes at Large $D$
• A Charged Membrane Paradigm at Large D
• Constraints on the effective fluid theory of stationary branes
• Emergent Supersymmetry in Local Equilibrium Systems
• Charged Black Rings at large D
• Surface transport in plasma-balls
• Charged rotating black holes at large D
• (Non)-Dissipative Hydrodynamics on Embedded Surfaces
• On the surface of superfluids
• The large D limit of dimensionally continued gravity
• Elastic instability of black rings at large D
• Schwinger-Keldysh superspace in quantum mechanics
• Instability of Charged Gauss-Bonnet Black Hole in de Sitter Spacetime at Large $D$
• On actions for (entangling) surfaces and DCFTs
• Non-spherically symmetric black string perturbations in the large D limit
• Lumps of plasma in arbitrary dimensions

Cited by in corpus (20)

• The Large D Limit of Einstein's Equations
• Rotating black holes and black bars at large D
• Black holes in presence of cosmological constant: Second order in 1/D
• Holographic Bjorken Flow at Large-D
• Stationary Solutions from the Large D Membrane Paradigm
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$
• Entropy production and entropic attractors in black hole fusion and fission
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity
• A leading-order comparison between fluid-gravity and membrane-gravity dualities
• Large D membrane for Higher Derivative Gravity and Black Hole Second Law
• Fluid-gravity and membrane-gravity dualities - Comparison at subleading orders
• The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant
• The large D effective theory of black strings in AdS
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Black hole interactions at large $D$: brane blobology
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit
• Stress Tensor for Large-$D$ membrane at subleading orders
• Schwarzschild-Tangherlini quasinormal modes at large $D$ revisited