Driven black holes: from Kolmogorov scaling to turbulent wakes

Abstract

General relativity governs the nonlinear dynamics of spacetime, including black holes and their event horizons. We demonstrate that forced black hole horizons exhibit statistically steady turbulent spacetime dynamics consistent with Kolmogorov’s theory of 1941. As a proof of principle we focus on black holes in asymptotically anti-de Sitter spacetimes in a large number of dimensions, where greater analytic control is gained. We focus on cases where the effective horizon dynamics is restricted to 2+1 dimensions. We also demonstrate that tidal deformations of the horizon induce turbulent dynamics. When set in motion relative to the horizon a deformation develops a turbulent spacetime wake, indicating that turbulent spacetime dynamics may play a role in binary mergers and other strong-field phenomena.

Large D black holes in an environment

“…The counterpart of our analysis in a spacetime with negative cosmological constants is equivalent to introducing deformations in the boundary metric of the spacetime. The effective equations in presence of boundary deformations in the mass momentum formalism has been computed in [20] and the fluid like behaviour of the corresponding non-gravitational system has been studied in [21]. To obtain equivalent results in the membrane formalism we will need to do the analysis in presence of strong curvature asymptotes (mentioned in the previous paragraph) in presence of cosmological constant.…”

Stochastic gravity and turbulence

“…The authors then demonstrated that this relation holds in the case where the apparent horizon was initially excited and then left to decay -corresponding to decaying turbulent flow. In recent years there has been a significant body of scrutinizing, and building on, the work of [6], see, e.g., [9][10][11][12][13][14][15][16][17][18][19]. Arguably, one of the main shortcomings of [6] is that it deals with decaying turbulence where the Kraichnan-Kolmogorov scaling relations are notoriously difficult to capture for a prolonged time.…”

“…Some of the aforementioned works have dealt with versions of driven holographic turbulence. In [13,14,16] the authors considered driven turbulent solutions to relativistic fluid dynamics and approximated a gravity solution therefrom, while in [18,19] turbulence was studied in the limit of a large number of dimensions. However, as far as we can see, whenever a stochastic driving force was introduced, it was inserted by hand arbitrarily modifying the holographic dictionary.…”

Stochastic gravity and turbulence

“…The authors then demonstrated that this relation holds in the case where the apparent horizon was initially excited and then left to decay-corresponding to decaying turbulent flow. In recent years there has been a significant body of work scrutinizing, and building on, the results of [6], see, e.g., [9][10][11][12][13][14][15][16][17][18][19]. Arguably, one of the main shortcomings of [6] is that it deals with decaying turbulence where the Kolmogorov scaling relations are notoriously difficult to capture for a prolonged time.…”

“…Put differently, a random driving force is dual to random boundary conditions for the dynamical fields, including the metric itself. While some of the aforementioned works ( [10,13,14,16,18,19] in particular, and also [20]) have dealt with driving forces, there is no work, to our knowledge, which properly deals with a dual gravitational setup with random boundary conditions for the metric. The current work aims to fill in this gap.…”