  We study the dynamical evolution of perturbations in the gravitational field
of a collapsing fluid star. Specifically, we consider the initial value problem
for a massless scalar field in a spacetime similar to the Oppenheimer-Snyder
collapse model, and numerically evolve in time the relevant wave equation. Our
main objective is to examine whether the phenomenon of parametric
amplification, known to be responsible for the strong amplification of
primordial perturbations in the expanding Universe, can efficiently operate
during gravitational collapse. Although the time-varying gravitational field
inside the star can, in principle, support such a process, we nevertheless find
that the perturbing field escapes from the star too early for amplification to
become significant. To put an upper limit in the efficiency of the
amplification mechanism (for a scalar field) we furthermore consider the case
of perturbations trapped inside the star for the entire duration of the
collapse. In this extreme case, the field energy is typically amplified at the
level ~ 1% when the star is about to cross its Schwarszchild radius.
Significant amplification is observed at later stages when the star has even
smaller radius. Therefore, the conclusion emerging from our simple model is
that parametric amplification is unlikely to be of significance during
gravitational collapse. Further work, based on more realistic collapse models,
is required in order to fully assess the astrophysical importance of parametric
amplification.
