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.
Highlights
The most widely celebrated results on the universality of turbulent cascades are captured by Kolmogorov’s theory of 1941 [13, 14] (K41).1 Under similarity hypotheses for homogeneous isotropic turbulence, the statistical distributions of the velocity field in the inertial range depend only on the rate of transfer of kinetic energy within the cascade, ε
We demonstrate that forced black hole horizons exhibit statistically steady turbulent spacetime dynamics consistent with Kolmogorov’s theory of 1941
In this paper we have worked at strictly infinite spacetime dimension, D, though we considered dynamics constrained to 2 + 1 of them
Summary
We shall record the most salient points regarding the effective theory that describes the dynamics of black branes in asymptotically AdSD spacetimes at large D, derived in [20,21,22,23] (see [34]). A mathematical simplification arises that allows us to solve the constraints in the radial direction, so that the basic variables can be readily related to the energy and momentum density of a fluid. All that remains is to provide the relations between these gravitational variables (a, pi), in which we carry out numerical evolution, and a set of fluid variables: the fluid energy density is a, whilst the velocity is vi = (pi − ∂ia)/a, see [24] for details Note that this large D limit results in a set of non-relativistic equations
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