  We study the dynamics of gravitationally collapsing massive shells in AdS
spacetime, and show in detail how one can determine extremal surfaces
traversing them. The results are used to solve the time evolution of the
holographic entanglement entropy in strongly coupled dual conformal gauge
theory, which is is seen to exhibit a regime of linear growth independent of
the shape of the boundary entangling region and the equation of state of the
shell. Our exact results are finally compared to those of two commonly used
approximation schemes, the Vaidya metric and the quasistatic limit, whose
respective regions of validity are quantitatively determined.
