Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence

TL;DR

This paper reviews the fluid-gravity correspondence within the AdS/CFT framework, illustrating how black hole solutions relate to fluid dynamics in strongly coupled conformal field theories, and discusses recent extensions to matter fields and non-relativistic systems.

Contribution

It provides a comprehensive overview of the geometric construction of fluid dynamics from black hole solutions and introduces recent advancements in the correspondence's scope.

Findings

Derived hydrodynamic transport coefficients from black hole geometries

Extended the fluid-gravity correspondence to include matter fields

Explored non-relativistic system applications

Abstract

We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluid-gravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in the strongly interacting boundary field theory. We explain how the geometric duals to the fluid dynamics are constructed in a boundary derivative expansion and use the construction to extract the hydrodynamic transport coefficients. In addition we also describe the recent developments extending the correspondence to incorporate matter fields and to non-relativistic systems. Based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge Theories, Geneva, Switzerland (February 2009).