  In this paper we study the evaporation of a four-dimensional spherically
symmetric black hole formed during a gravitational collapse, analyzing the
backreaction of a massless conformally coupled quantum scalar field by means of
the semiclassical Einstein equation. We link the evaporation and the
corresponding black hole mass loss to an ingoing negative energy flux at the
dynamical horizon and we show how the quantum matter trace anomaly sources that
flux once a suitable averaged energy condition is assumed outside the black
hole horizon. This condition is satisfied by the background matter in most
realistic classical models of spherically symmetric stellar collapse. Finally,
as an example, we evaluate explicitly the negative ingoing flux and the
corresponding rate of evaporation in case of a null radiating star described by
the Vaidya spacetime.
