Nonlinear Fluid Dynamics from Gravity

TL;DR

This work derives nonlinear boundary fluid dynamics from gravity in AdS$_5$ by promoting the black brane temperature and velocity to boundary fields and solving Einstein's equations perturbatively in a boundary derivative expansion. The authors construct the dual bulk metric and compute the boundary stress tensor to second order, establishing Weyl invariance and obtaining explicit second-order transport coefficients (e.g., $\tau_\Pi$, $\lambda_1$, $\lambda_2$, with $\lambda_3=0$ and $\kappa$ undetermined) that match independent analyses. They also derive the dispersion relations for sound and shear modes and demonstrate universality of the fluid description for conformal theories with gravitational duals, including a detailed comparison with Baier et al. The results provide a concrete, gravitational derivation of nonlinear fluid dynamics and a framework for exploring holographic hydrodynamics and its phenomenological implications.

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.