  In this work we describe the partial collapse of a compact object and the
emission of spacetime waves as a result of back-reaction effects. As a source
mass term we propose a non-smooth continuous function that describes a
mass-loss, and we then obtain the solution of such setting. We present three
distinct examples of the evolution of the norm $|R_{nl}(t,r_{*})|$ in terms of
$t$, and four different results are shown for the parameter $l=1,2,5,10$; here
$r_{*}$ is the fixed radius of an observer outside the compact object. In all
cases, the decay behaviour is actually present at $t\gg 1$ and becomes more
evident for larger $l$. In addition, for the results that have smaller $l$'s
their amplitudes are larger when the asymptotic character of
$|R_{nl}(t,r_{*})|$ clearly appears. Finally, the farther away an observer is
set, the fewer oscillations are perceived; however, from our particular fixed
set of parameters, the best spot to observe the wiggles of the emitted
spacetime waves is close to $r_{*}\simeq \alpha$.
