Space-time waves from a collapse with a time dependent cosmological parameter

We study the emission of space-time waves produced by back-reaction effects during a collapse of a spherically symmetric universe with a time dependent cosmological parameter, which is driven by a scalar field. As in a previous work the final state avoids the final singularity due to the fact the co-moving relativistic observer never reaches the center, because the physical time evolution $d\tau=U_{0}\,dx^0$, decelerates for a co-moving observer which falls with the collapse. The equation of state of the system depends on the rate of the collapse, but always is positive: $0 < \omega(p) < 0.25$.