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

In a previous article the Einstein-Maxwell field equations for non-null electromagnetic fields were studied under the conditions that the null tetrad is parallel-propagated along both principal null congruences. A solution with twist and shear, but no expansion, was found and was conjectured to be the only expansion-free solution. Here it is shown that this conjecture is false; the general expansion-free solution is found to be a family of space-times depending on a single constant parameter which is the ratio of the (constant) twists of the two principal null congruences.We are grateful to R. G. McLenaghan and N. Tariq for kindly informing us that they have found essentially the same solution. Their article appeared recently inJournal of Mathematical Physics.