  Using a framework based on the 1+3 formalism, we show that a source
represented by a geodesic, dissipative, rotational dust, endowed with axial and
reflection symmetry, violates regularity conditions at the center of the fluid
distribution, unless the dissipative flux vanishes. In this latter case the
vorticity also must vanish, and the resulting spacetime is
Friedman--Robertson--Walker (FRW). Therefore it does not produce gravitational
radiation.
