Nonlinear Fluid Dynamics from Gravity

TL;DR

This paper derives the nonlinear equations governing boundary fluid dynamics from gravity by promoting black brane parameters to dynamic fields and solving Einstein's equations, providing explicit second-order stress tensor expressions.

Contribution

It presents a derivation of nonlinear boundary fluid equations from gravity, valid for arbitrary amplitudes, with explicit second-order stress tensor results.

Findings

Derived nonlinear boundary fluid equations from gravity.

Explicit second-order fluid stress tensor expression.

Valid for arbitrary amplitudes in boundary derivative expansion.

Abstract

Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields -- arbitrary functions of the coordinates on the boundary of AdS5 -- we use Einstein's equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.