Event horizons and apparent horizons in spherically symmetric geometries.

Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, have a fixed area and must propagate outward with a velocity equal to the velocity of radially outgoing photons. That proves, within the framework of the (1+3) formalism and without resorting to the Birkhoff theorem, that apparent horizons coincide with event horizons in electrovacuum.