Spherically symmetric space–times with constant curvature scalar

In view of the geometrical importance of spaces with constant scalar curvature, a systematic study of spherically symmetric such space–time manifolds with respect to the eigenvalues of the Ricci tensor is made. The cases of two double or one quadruple eigenvalue are treated exhaustively. In the generic case of one double and two single eigenvalues, no conformally flat solutions, and only solutions with one arbitrary function of one variable are found. We also give all four-dimensional decomposable s.s. spaces with constant curvature scalar.