On the conformal transformation between two anisotropic fluid spacetimes

Abstract

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.