  We derive in detail several universal features in the time evolution of
entanglement entropy and other nonlocal observables in quenched holographic
systems. The quenches are such that a spatially uniform density of energy is
injected at an instant in time, exciting a strongly coupled CFT which
eventually equilibrates. Such quench processes are described on the gravity
side by the gravitational collapse of a thin shell that results in a black
hole. Various nonlocal observables have a unified description in terms of the
area of extremal surfaces of different dimensions. In the large distance limit,
the evolution of an extremal surface, and thus the corresponding boundary
observable, is controlled by the geometry around and inside the event horizon
of the black hole, allowing us to identify regimes of pre-local- equilibration
quadratic growth, post-local-equilibration linear growth, a memory loss regime,
and a saturation regime with behavior resembling those in phase transitions. We
also discuss possible bounds on the maximal rate of entanglement growth in
relativistic systems.
