  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 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.
