A seminumeric method by Herrera, Jimenez and Ruggeri is used to study
the evolution of general relativistic spheres in the free streaming ra
diation approximation, when specific contraction schemes are imposed a
nd for particular oscillatory radiation profiles. On one hand, the eme
rging radiation is studied for oscillating contracting spheres, on the
other, the variation of the boundary surface is analyzed when a pulsa
ting profile is provided. We consider three particular equations of st
ate previously studied. It is found that the oscillatory frequency of
the surface for the equations of state considered coincides with the f
requency of the oscillation for the radiation profile.