The optical scalars in Kerr-Schild-type spacetimes

The optical scalars are defined and the optical equations are derived for a null, geodesic, but not necessarily affinely parametrized, vector field. The optical scalars are left invariant under the action of a Kerr-Schild-type transformation $\text{g}\text{?}{}_{\mathrm{ab}}\text{= g}{}_{\mathrm{ab}}\text{+ l}{}_{\mathrm{a}}\text{l}{}_{\mathrm{b}}$. The optical equations are integrated explicitly in Kerr-Schild-type spacetimes. As an application, the search for Kerr-Schild-type N spacetimes with twisting rays is formulated.