  It is shown that the evolution of an axially and reflection symmetric fluid
distribution, satisfying the Tolman condition for thermal equilibrium, is not
accompanied by the emission of gravitational radiation. This result, which was
conjectured by Bondi many years ago, expresses the irreversibility associated
to the emission of gravitational waves. The observational consequences emerging
from this result are commented. The resulting models are not only
non--dissipative and vorticity free, but also shear--free and geodesic,
furthermore all their complexity factors vanish.
