KS-related f-g couples as exact vacuum solutions of Salam's two-tensor theory

The exact solutions of the vacuum field equations of the two-tensor theory of gravitation proposed by Salam et al. are determined for the case that the two tensors differ only by the tensor product of a null vector field with itself. It is found that this null vector field must be geodesic with vanishing shear, expansion, and twist, and represents a field of multiple principal null directions for both Weyl tensors. As a consequence, the solutions can be derived from the results of a paper by Kundt.