  We study the partial time dependent collapse of a spherically symmetric
compact object with initial mass $M_1+M_2$ and final mass $M_2$ and the waves
of space-time emitted during the collapse via back-reaction effects. We obtain
exact analytical solutions for the waves of space-time in an example in which
$M_1=M_2=(M_1+M_2)/2$. The wavelengths of the space-time emitted waves during
the collapse have the cut (we use natural units $c=\hbar=1$): $\lambda <
(2/b)$, $(1/b)$-being the time scale that describes the decay of the compact
object.
