Linearly resummed hydrodynamics in a weakly curved spacetime

TL;DR

This paper extends all-order linearly resummed hydrodynamics to weakly curved spacetimes using AdS/CFT, revealing new curvature-induced transport coefficients and providing analytical and numerical results for these coefficients.

Contribution

It introduces a framework for all-order hydrodynamics in weakly curved backgrounds, including new curvature-coupled transport coefficients, with analytical and numerical computations.

Findings

Identification of four new curvature-induced transport coefficients.

Analytical computation of coefficients in the hydrodynamic limit.

Numerical evaluation of coefficients at large momenta.

Abstract

We extend our study of all-order linearly resummed hydrodynamics in a flat space~\cite{1406.7222,1409.3095} to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically \emph{locally} $\textrm{AdS}_5$ geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs.~\cite{1406.7222,1409.3095}, we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref.~\cite{0905.4069}, the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.