The late-time attractor structure of dynamical black branes

The ringdown phase of a perturbed black hole is conventionally described by a linear superposition of quasinormal modes. However, as the AdS black brane approaches its final global equilibrium, this linear quasinormal mode description becomes inadequate, and nonlinear dynamics play a significant role in the late-stage evolution. We show that the interplay between nonlinear evolution and horizon dissipation in general relativity drives dynamical AdS black branes towards the final state along a unique path, independent of their initial perturbations. Through numerical simulations, we identify this late-time attractor and uncover the associated universal nonlinear behavior, characterized by a simple dimensionless relative amplitude in the dual hydrodynamic variables.