A kinematic method to obtain conformal factors

Radial conformal motions are considered in conformally flat space-times and their properties are used to obtain conformal factors. The geodesic case l eads directly to the conformal factor of Robertson-Walker universes. Genera l cases admitting homogeneous expansion or orthogonal hypersurfaces of cons tant curvature are analyzed separately. When the two conditions above are c onsidered together a subfamily of the Stephani perfect fluid solutions, wit h acceleration Fermi-Walker propagated along the flow of the fluid, follows . The corresponding conformal factors are calculated and contrasted with th ose associated with Robertson-Walker space-times. (C) 2000 American Institu te of Physics. [S0022-2488(00)03007-3].