  A relativistic model for the emission of gravitational waves from an
initially unperturbed Schwarzschild black hole, or spherical collapsing
configuration, is completely integrated. The model consists basically of
gravitational perturbations of the Robinson-Trautman type on the Schwarzschild
spacetime. In our scheme of perturbation, gravitational waves may extract mass
from the collapsing configuration. Robinson-Trautmann perturbations also
include another mode of emission of mass, which we denote shell emission mode:
in the equatorial plane of the configuration, a timelike $(1+2)$ shell of
matter may be present, whose stress-energy tensor is modelled by neutrinos and
strings emitted radially on the shell; no gravitational waves are present in
this mode. The invariant characterization of gravitational wave perturbations
and of the gravitational wave zone is made through the analysis of the
structure of the curvature tensor and the use of the Peeling Theorem.
