Space-time waves from a collapsing universe with a gravitational attractor

We study a collapsing system attracted by a spherically symmetric gravitational source, with an increasing mass, that generates back-reaction effects that are the source of space-time waves. As an example, we consider an exponential collapse and the space-time waves emitted during this collapse due to the back-reaction effects, originated by geometrical deformation driven by the increment of the gravitational attracting mass during the collapse.