SHEAR-FREE SPHERICALLY SYMMETRICAL PERFECT FLUID SOLUTIONS WITH CONFORMAL SYMMETRY

In 1987, Dyer, McVittie and Oattes determined the general relativistic field equations for a shear-free perfect fluid with spherical symmetry and a conformal Killing vector in the t-r plane, which depend on an arbitrary constant m. Two particular solutions of these equations were given recently by Maharaj, Leach and Maartens, as well as a partial solution thought to be valid for almost all m. In this paper, this solution is completed for four values of m, and it is shown that it cannot be completed for any others by currently available techniques; however, a new solution of a different form, but also depending on a Weierstrass elliptic function, is found for a further value of m. None of these metrics are conformally flat; one of them has a constant expansion rate.