Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The fluid/gravity correspondence

Veronika E. Hubeny, Shiraz Minwalla, Mukund Rangamani

TL;DR

The paper establishes and elaborates the fluid/gravity correspondence, showing that the long-wavelength limit of Einstein gravity with negative cosmological constant is dual to d-dimensional relativistic hydrodynamics. It develops a systematic gradient expansion to construct dual bulk geometries from slowly varying boundary data and derives the boundary stress tensor and a physically meaningful entropy current from the bulk horizon. The authors compute second-order dissipative transport coefficients for conformal fluids, discuss extensions to non-conformal and charged fluids, and connect the framework to broader developments such as the Israel-Stewart formalism, the membrane paradigm, and blackfolds. The work provides a powerful, non-perturbative tool to study strongly coupled fluids via gravitational dynamics and offers insights into holographic descriptions of real-world viscous systems.

Abstract

We review the fluid/gravity correspondence which relates the dynamics of Einstein's equations (with negative cosmological constant) to the dynamics of relativistic Navier-Stokes equations.

The fluid/gravity correspondence

TL;DR

The paper establishes and elaborates the fluid/gravity correspondence, showing that the long-wavelength limit of Einstein gravity with negative cosmological constant is dual to d-dimensional relativistic hydrodynamics. It develops a systematic gradient expansion to construct dual bulk geometries from slowly varying boundary data and derives the boundary stress tensor and a physically meaningful entropy current from the bulk horizon. The authors compute second-order dissipative transport coefficients for conformal fluids, discuss extensions to non-conformal and charged fluids, and connect the framework to broader developments such as the Israel-Stewart formalism, the membrane paradigm, and blackfolds. The work provides a powerful, non-perturbative tool to study strongly coupled fluids via gravitational dynamics and offers insights into holographic descriptions of real-world viscous systems.

Abstract

We review the fluid/gravity correspondence which relates the dynamics of Einstein's equations (with negative cosmological constant) to the dynamics of relativistic Navier-Stokes equations.

Paper Structure

This paper contains 30 sections, 53 equations, 1 figure.

Table of Contents

  1. The fluid/gravity correspondence
  2. Introduction
  3. Prelude: CFT stress tensor dynamics from gravity
  4. Preview of the fluid/gravity correspondence
  5. Relativistic fluid dynamics
  6. The equations of fluid dynamics and constitutive relations
  7. The Navier-Stokes scaling limit
  8. Perturbative construction of gravity solutions
  9. Global thermal equilibrium from gravity
  10. The perturbation theory
  11. Results at 2nd order
  12. Weyl-covariant formalism
  13. Generic asymptotically AdS black hole metric
  14. Event horizon and entropy current
  15. Stress tensor of dissipative fluid
  16. ...and 15 more sections

Figures (1)

  • Figure 1.1: Penrose diagram of the uniform planar black hole (\ref{['sads1']}) and the causal structure of the spacetimes dual to fluid dynamics illustrating the tube structure. Dashed line in the second figure denotes the future event horizon, while the shaded tube indicates the region of spacetime over which the solution is well approximated by a corresponding uniform black hole.