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 a 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 we quantitatively determine.

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