We investigate the necessary conditions for the two spacetimes, which are solutions to the Einstein field equations with an anisotropic matter source, to be related to each other by means of a conformal transformation. As a result, we obtain that if one of such spacetimes is a generalization of the Robertson-Walker solution with vanishing acceleration and vorticity, then the other one has to be in this class as well, i.e. the conformal factor will be a constant function on the hypersurfaces orthogonal to the fluid flow lines. The evolution equation for this function appears naturally as a direct consequence of the conformal transformation of the Ricci tensor.
Categories: gr-qc