Holographic Path to the Turbulent Side of Gravity


We study the dynamics of a $2+1$-dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the “gravity/fluid correspondence,” to $3+1$-dimensional asymptotically anti–de Sitter (AAdS) black-brane solutions to the Einstein equation. We examine stability properties of shear flows, which correspond to hydrodynamic quasinormal modes of the black brane. We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long-wavelength modes. We then map this fluid solution, via the gravity/fluid duality, into a bulk metric. This suggests a new and interesting feature of the behavior of perturbed AAdS black holes and black branes, which is not readily captured by a standard quasinormal mode analysis. Namely, for sufficiently large perturbed black objects (with long-lived quasinormal modes), nonlinear effects transfer energy from short- to long-wavelength modes via a turbulent cascade within the metric perturbation. As long-wavelength modes have slower decay, this transfer of energy lengthens the overall lifetime of the perturbation. We also discuss various implications of this behavior, including expectations for higher dimensions and the possibility of predicting turbulence in more general gravitational scenarios.

Phys. Rev. X 4, 011001