Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions

TL;DR

This paper develops a general framework connecting conformal fluid dynamics with gravity in arbitrary dimensions, providing explicit formulas for stress tensors, metrics, and entropy currents, and relating black hole solutions to fluid flows.

Contribution

It extends the fluid/gravity correspondence to arbitrary dimensions, offering explicit expressions for dual metrics and stress tensors up to second order in derivatives.

Findings

Explicit stress tensor and metric formulas for arbitrary dimensions.

Reformulation of rotating black holes as fluid flows.

Agreement of black hole solutions with fluid dynamical metrics.

Abstract

We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdS_{d+1} long wavelength solutions of Einstein's equations with a negative cosmological constant, for all d>2. We find simple explicit expressions for the stress tensor (slightly generalizing the recent result by Haack and Yarom (arXiv:0806.4602)), the full dual bulk metric and an entropy current of this strongly coupled conformal fluid, to second order in the derivative expansion, for arbitrary d>2. We also rewrite the well known exact solutions for rotating black holes in AdS_{d+1} space in a manifestly fluid dynamical form, generalizing earlier work in d=4. To second order in the derivative expansion, this metric agrees with our general construction of the metric dual to fluid flows.