  We compute the time-dependent entanglement entropy of a CFT which starts in
relatively simple initial states. The initial states are the thermofield double
for thermal states, dual to eternal black holes, and a particular pure state,
dual to a black hole formed by gravitational collapse. The entanglement entropy
grows linearly in time. This linear growth is directly related to the growth of
the black hole interior measured along "nice" spatial slices. These nice slices
probe the spacelike direction in the interior, at a fixed special value of the
interior time. In the case of a two-dimensional CFT, we match the bulk and
boundary computations of the entanglement entropy. We briefly discuss the long
time behavior of various correlators, computed via classical geodesics or
surfaces, and point out that their exponential decay comes about for similar
reasons. We also present the time evolution of the wavefunction in the tensor
network description.
