Einstein--Maxwell fields of the Kerr--Schild and generalized Kerr--Schild class

The Einstein and Einstein-Maxwell gravitational field equations were studied using the null tetrad formalism of Debney, Kerr, and Schild. Vacuum gravitational field equations were derived for the class of metrics conformally related to Kerr--Schild metric with geodesic null rays. It was found that all such metrics are necessarily algebraically special. A partial integration of the vacuum field equations was achieved by imposing restrictions on the conformal factor. A new class of algebraically special Einstein-Maxwell spacetimes was discovered by imposing a new assumption on the electrovac field equations derived by Debney, Kerr, and Schild for metrics of the Kerr-Schild form. A special member of the class is a new twisting, axially symetric one parameter generalization of the Reissner-Nordstrom solution. It is singular in a bounded region and asymptotically flat. The singularity, which is naked, defines a ring in the auxiliary Minkowski space whose radius depends linearly on time. The electromagnetic fields correspond asymptotically, in the limit of small twist, to those arising from a point charge and a linearly time dependent magnetic dipole. The angular momentum associated with the axial Killing vector vanishes, despite the presence of twist in the degenerate principal null vector field. This was taken as evidence that the mass monopole also vanishes. A coordinate transformation was constructed which relates the physically interesting special solution to the field equations derived by Lind. A theorem of Lind's on regular asymptotically flat algebraically special spacetimes was shown by explicit counterexample to hold only in the case of nonvanishing mass monopole