Fluid spacetimes admitting a conformal Killing vector parallel to the velocity vector

The author proves the result that any perfect fluid solution of Einstein's field equations satisfying a barotropic equation of state p=p( mu ) and the condition mu +p not=O, which admits a proper conformal Killing vector (CKV) parallel to the fluid 4-velocity, is locally a Friedmann-Robertson-Walker model. Generalizations of this result to the case p not=p( mu ) are then investigated. Finally, the consequences of the result are discussed and related to previous work on inheriting CKV, on asymptotic Friedmann-like CKV, on a conjecture that shear-free, perfect fluid models necessarily have either zero vorticity or zero expansion, and previous results from relativistic kinetic theory.