The holographic fluid dual to vacuum Einstein gravity

TL;DR

This paper develops a systematic method to reconstruct vacuum Einstein gravity solutions from a dual fluid description, extending previous hydrodynamic expansions to all orders and analyzing the properties of the dual fluid and its transport coefficients.

Contribution

It introduces an algorithm for higher-order reconstruction of Einstein solutions from fluid dynamics, including explicit metric and stress tensor results, and explores the dual fluid's unique properties.

Findings

Explicit bulk metric and stress tensor up to fifth order

Dual fluid obeys incompressible Navier-Stokes with higher derivatives

Identifies transport coefficients and constraints of the holographic fluid

Abstract

We present an algorithm for systematically reconstructing a solution of the (d+2)-dimensional vacuum Einstein equations from a (d+1)-dimensional fluid, extending the non-relativistic hydrodynamic expansion of Bredberg et al in arXiv:1101.2451 to arbitrary order. The fluid satisfies equations of motion which are the incompressible Navier-Stokes equations, corrected by specific higher derivative terms. The uniqueness and regularity of this solution is established to all orders and explicit results are given for the bulk metric and the stress tensor of the dual fluid through fifth order in the hydrodynamic expansion. We establish the validity of a relativistic hydrodynamic description for the dual fluid, which has the unusual property of having a vanishing equilibrium energy density. The gravitational results are used to identify transport coefficients of the dual fluid, which also obeys an interesting and exact constraint on its stress tensor. We propose novel Lagrangian models which realise key properties of the holographic fluid.