Axisymmetric Stationary Spacetimes of Constant Scalar Curvature in Four   Dimensions
  In this paper we construct a special class of four dimensional axisymmetric stationary spacetimes whose Ricci scalar is constant but not Einstein. We find that this solution has a ring singularity. At the end, we discuss some numerical results of these spacetimes. 
Rosikhuna F. Assafari, Emir S. Fadhilla, Bobby E. Gunara, Hasanuddin,   and Abednego Wiliardy
gr-qc hep-th