  We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS)
spacetime by solving numerically the four-dimensional spherically symmetric
Einstein-massless-scalar field equations with negative cosmological constant.
Our results suggest that AdS spacetime is unstable under arbitrarily small
generic perturbations. We conjecture that this instability is triggered by a
resonant mode mixing which gives rise to diffusion of energy from low to high
frequencies.
