  The evolution of spheroids of matter emitting gravitational waves and null
radiation field is studied in the realm of radiative Robinson-Trautman
spacetimes. The null radiation field is expected in realistic gravitational
collapse, and can be either an incoherent superposition of waves of
electromagnetic, neutrino or massless scalar fields. We have constructed the
initial data identified as representing the exterior spacetime of uniform and
non-uniform spheroids of matter. By imposing that the radiation field is a
decreasing function of the retarded time, the Schwarzschild solution is the
asymptotic configuration after an intermediate Vaidya phase. The main
consequence of the joint emission of gravitational waves and the null radiation
field is the enhancement of the amplitude of the emitted gravitational waves.
Another important issue we have touched is the mass extraction of the bounded
configuration through the emission of both types of radiation.
