Holographic Path to the Turbulent Side of Gravity

Abstract

We study the dynamics of a 2 þ 1-dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the ''gravity/fluid correspondence,'' to 3 þ 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.

Quasinormal Modes Beyond Kerr

“…In addition, modes of lower frequencies are driven by modes with higher frequencies. This situation is analogous to the recently discovered turbulent behavior of perturbations of 4-dimensional AdS black hole spacetimes [1] and their 3-dimensional conformal fluid duals [4], which feature an inverse cascade of mode energy to lower frequencies. In fact, it is the connection to the fluid-gravity correspondence that first motivated the study of the parametric instability, which may represent the onset of turbulence around a rapidly rotating black hole [11].…”

Numerical measurements of scaling relations in two-dimensional conformal fluid turbulence

“…There has been some work on the analytical front [1,22,23] and several numerical investigations [1,13,[24][25][26][27][28][29][30][31]. Because correlation functions can indeed be measured in relevant scenarios -perhaps even in QG plasma [8,9,[32][33][34] -and interesting implications for the gravitational field follow from holography, it is of interest to further investigate relativistic turbulence.…”

“…The (2 + 1)-dimensional case is especially relevant to draw intuition for related phenomena in (3 + 1)-dimensional gravity with the help of the fluid-gravity correspondence (e.g. [12,16,25]). This work is largely a continuation and completion of [1], which contained a numerical study which was inconclusive at the time.…”

“…having a very large sound speed and no mass density), and its turbulent regime is seldom studied (see eg. [13,25]), so one may not expect the same energy spectra a priori. We elaborate more on this in section 5, where we demonstrate that the k −2 spectrum is not necessarily associated with compressive effects.…”

Scaling relations in two-dimensional relativistic hydrodynamic turbulence

“…In the present work, we add to a handful of steps already taken to understand relativistic turbulence [9][10][11][12][13][14][15][16] by performing both analytical and numerical analysis of such fluid flows, placing particular emphasis on two spatial dimensions. In part, we build upon previous work by Fouxon and Oz [9], who derived some scaling relations for relativistic hydrodynamic turbulence applicable to d ≥ 3 spatial dimensions.…”