On uniqueness of non-vacuum stationary axisymmetric type D spacetime

We study a family of the non-vacuum stationary axisymmetric type D metrics, where the two principal null directions are geodesic and shearfree. It is demonstrated that the conformal-to-Carter metric gives the most general form of this family, without any assumptions which are previously used by Ovcharenko and Podolský to arrive at this conclusion.