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 dτ=U0dx0, 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<ω(p)