The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm

TL;DR

The Fluid/Gravity correspondence links Einstein's equations in higher dimensions to fluid dynamics, enabling the construction of black hole spacetimes from fluid solutions, with broad applications in theoretical physics.

Contribution

It introduces a novel framework connecting gravity and fluid dynamics via gauge/gravity duality, providing a systematic way to generate black hole solutions from fluid flows.

Findings

Mathematically relates Einstein's equations to Navier-Stokes equations.

Allows construction of black hole spacetimes from fluid solutions.

Enables new applications in understanding gravity and gauge theories.

Abstract

This talk gives an overview of the recently-formulated Fluid/Gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in d+1 dimensions capture the (generalized) Navier-Stokes equations in d dimensions. Given an arbitrary fluid dynamical solution, we can systematically construct a corresponding asymptotically AdS black hole spacetime with a regular horizon whose properties mimic that of the fluid flow. Apart from an overview of this construction, we describe some of its applications. The presentation is intended for a broad audience of relativists, and does not assume prior knowledge of string theory or gauge/gravity duality.