Shearing and geodesic axially symmetric perfect fluids that do not
  produce gravitational radiation
  Using a framework based on the 1+3 formalism we carry out a study on axially
and reflection symmetric perfect and geodesic fluids, looking for possible
models of sources radiating gravitational waves. Therefore, the fluid should be
necessarily shearing, for otherwise the magnetic part of the Weyl tensor
vanishes, leading to a vanishing of the super-Poynting vector. However, for the
family of perfect, geodesic fluids considered here, it appears that all
possible cases reduce to conformally flat, shear--free, vorticity-free, fluids,
i.e Friedmann-Roberston-Walker. The super-Poynting vector vanishes and
therefore no gravitational radiation is expected to be produced. The physical
meaning of the obtained result is discussed.
