Equilibrium distributions of the charged fluids in the space-times with a simple-transitive groups of homothetic motions

The method of finding of the exact solutions of the self-consistent Einstein–Maxwell equations system are suggested. It is supposed that the space-time admits simple-transitive group of homothetic transformations and the source of such space-times is the perfect fluid. The proposed method is the generalization of Ozsvath's method of finding of the homogeneous solutions of Einstein field equations. It is supposed also that the fluid's velocity vector is collinear to time-like vector $\mathbf Y$ of the Lie algebra of the group $H_r.$ Under above assumption all exact solutions of the system are found.