Relativistic shear-free fluids with symmetry

We study the complete conformal geometry of shear-free spacetimes with spherical symmetry and do not specify the form of the matter content. The equation governing the general conformal Killing symmetry is solved, and we explicitly exhibit the conformal vector. The existence of a conformal symmetry places restrictions on the model. The conditions on the gravitational potentials are expressed as a system of integrability conditions. Timelike sectors and inheriting conformal symmetry vectors, which map fluid flow lines conformally onto fluid flow lines, are generated, and the integrability conditions are shown to be satisfied. As an example, a spacetime, which is expanding and accelerating, is identified that contains a spherically symmetric conformal symmetry.