Abstract
The Nijenhuis tensorsNab••c corresponding to the different types of relativistic electromagnetic fields in the Ruse-Synge classification are considered. By using the Newman-Penrose spin coefficient formalism, it is shown that for the type-A fieldsNab••c=0 if and only if i) all the optical parameters of the two real null congruencesla andna vanish and ii)la;bnb=na;blb=0. In the case of the type-B fields,Nab••c=0 if and only if i)la is twist free,la;bnb=0, and ii)\(I_1 = \varrho \bar \varphi _2 \). The conditions for the type-C fields are obtainable from the type-B fields by just interchangingla withna. The effect ofNab••c=0 on the 4-currentJa is that i)Ja=0 for the type-A′ field and ii)JaJa<0 for the type-A″ field as well as for the singular fields (typeB and typeC).
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