In , it was shown that the Newman-Janis translation works for algebraically special metrics which belong to the Kerr-Schild class  and can be presented as [g.sub.[mu]v] = [[eta].sub.[mu]v] + 2f(r)[k.sub.[mu][k.sub.v], where [[eta].sub.[mu]v] is the Minkowski metric and [k.[mu]] are principal null congruences.
Gurses and Gursey have found that the algebraically special metrics of the Kerr-Schild class can be presented in the Lorentz covariant coordinate system, developed the general approach based on the complex Trautman-Newman techniques (which include the Newman-Janis translation), and derived the axially symmetric metric in the general, model-independent form.