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 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.
%0 Generic
%1 citeulike:12685892
%A Green, Stephen R.
%A Carrasco, Federico
%A Lehner, Luis
%D 2013
%K imported
%T A Holographic Path to the Turbulent Side of Gravity
%U http://arxiv.org/abs/1309.7940
%X 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 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.
@misc{citeulike:12685892,
abstract = {{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 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.}},
added-at = {2019-03-25T08:20:55.000+0100},
archiveprefix = {arXiv},
author = {Green, Stephen R. and Carrasco, Federico and Lehner, Luis},
biburl = {https://www.bibsonomy.org/bibtex/212a53e9789fa00844fa591a37e5bed5a/ericblackman},
citeulike-article-id = {12685892},
citeulike-linkout-0 = {http://arxiv.org/abs/1309.7940},
citeulike-linkout-1 = {http://arxiv.org/pdf/1309.7940},
day = 30,
eprint = {1309.7940},
interhash = {ee539a8ae1bbf747a05fc1d41b0d4185},
intrahash = {12a53e9789fa00844fa591a37e5bed5a},
keywords = {imported},
month = sep,
posted-at = {2013-10-03 05:46:12},
priority = {2},
timestamp = {2019-03-25T08:20:55.000+0100},
title = {{A Holographic Path to the Turbulent Side of Gravity}},
url = {http://arxiv.org/abs/1309.7940},
year = 2013
}