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482 31 Non-diverging solutions (Kundt’s class)which has the general solutionP 2 = κ 0 |F | 2 (1 + ff) 2 (f ,ζ f ,ζ) −1 , f = f(ζ,u), (31.54)containing an arbitrary function f(ζ,u).Hacyan and Plebański (1975) investigated the subcase W = 0. Thefunctions Φ 0 2 ,G0 ,H 0 , inΦ 1 = F (ζ,u), Φ 2 = P F ,ζv +Φ 0 2, H = κ 0 F Fv 2 + G 0 v + H 0 , (31.55)with P given by (31.54), are then subject to the rest of the Einstein–Maxwell equations, i.e. to( Φ02 /P ) ,ζ(FP = −2) , [ G 0 ]+(lnP ) ,u,u ,ζ =2κ 0F Φ 0 2/P,P 2 H 0 + ,ζζ G0 (ln P ) ,u + (ln P ) ,uu − (ln P ),u 2 = κ 0 Φ 0 2 Φ 0 2 . (31.56)An obvious particular solution is given byds 2 =2dζdζ(1 + ff) −2 − 2du[dv +(f ′ f ′ v 2 + H 0 )du], f = f(ζ),√ (31.57)κ0 Φ 1 = f ′ = √ √κ 0 F, κ0 Φ 2 =(1+ff)f ′′ v, H 0 ,ζζ =0.From (31.28), this metric is of Petrov type III if f ′′ ̸= 0. The electromagneticfield is determined up to a constant duality rotation. Otherparticular solutions of (31.56) are given in Hacyan and Plebański(1975).Solutions with W ̸= 0,P ,u =0=G 0 =Φ 2 and constant κ 0 Φ 1 Φ 1 (andcosmological constant Λ) have been constructed by Khlebnikov (1986).It is a general feature of the type III solutions (aligned case) that thesecond eigendirection of the electromagnetic non-null field is not parallelto the single principal null direction of the Weyl tensor.A class of type D Einstein–Maxwell fields can be obtained from thegeneral type D vacuum class (31.41) by simply modifying the functionP 2 toP 2 =(z 2 + l 2 )[k(z 2 − l 2 )+2mz − e 2 ] −1 , (31.58)the rest of the metric remaining unchanged. The tetrad components ofthe electromagnetic field tensor are then√ eΦ 0 =0, 2κ0 Φ 1 =(z − i l) 2 , √ −2ezvκ0 Φ 2 =P (z − i l) 2 (z 2 + l 2 ) .(31.59)The two null eigendirections of the Maxwell field coincide with the eigendirectionsof the type D Weyl tensor. Like their uncharged counterparts