  Dark energy stars are finite size astrophysical objects with an interior
equation of state typical of dark energy. Examples are self-gravitating false
vacuum bubbles, vacuum non-singular black holes, and gravastars. We present a
time-dependent solution of Einstein's field equations that describes the
collapse of a spherical system from an initial state of positive pressure to a
final state with a dark energy core. Our solution has no singularities, no
event horizons, and does not violate the weak or null energy conditions.
