Physical infeasibility of geodesic dissipative dust as a source of gravitational radiation

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.