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We describe the transition of a graviationally radiating, axially andreflection symmetric dissipative fluid, to a non--radiating state. It is shownthat very shortly after the end of the radiating regime, at a time scale of theorder the thermal relaxation time, the thermal adjustment time and thehydrostatic time (whichever is larger), the system reaches the equilibriumstate. This result is at variance with all the studies carried out in the past,on gravitational radiation outside the source, which strongly suggest thatafter a radiating period, the conditions for a return to a static case, lookrather forbidding. As we shall see, the reason for such a discrepancy residesin the fact that some elementary, but essential, physical properties of thesource, have been overlooked in these latter studies.

The transition of a gravitationally radiating, dissipative fluid, to equilibrium