Parametric amplification of waves during gravitational collapse: a first investigation

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.