A class of algebraically general solutions of the Einstein-Maxwell equations for non-null electromagnetic fields

The Einstein-Maxwell field equations for non-null electromagnetic fields are studied under the conditions that the null tetrad is parallelly propagated along both principal null congruences. It is shown that the resulting spacetime solutions are necessarily algebraically general. The twist-free solution found in a previous article is shown to be the most general twist-free solution. An expansionfree solution with twist and shear is also found.