Contents

Contentsxv29.2 Some general classes of solutions 44229.2.1 Characterization of the known classes of solutions 44229.2.2 The case ∂ ζ I = ∂ ζ (G 2 − ∂ ζ G) ̸= 0 44529.2.3 The case ∂ ζ I = ∂ ζ (G 2 − ∂ ζ G) ̸= 0,L ,u = 0 44629.2.4 The case I = 0 44729.2.5 The case I =0=L ,u 44929.2.6 Solutions independent of ζ and ζ 45029.3 Solutions of type N (Ψ 2 =0=Ψ 3 ) 45129.4 Solutions of type III (Ψ 2 =0, Ψ 3 ̸= 0) 45229.5 Solutions of type D (3Ψ 2 Ψ 4 =2Ψ 2 3 , Ψ 2 ̸= 0) 45229.6 Solutions of type II 45430 Twisting Einstein–Maxwell and pure radiationfields 45530.1 The structure of the Einstein–Maxwell field equations 45530.2 Determination of the radial dependence of the metric and theMaxwell field 45630.3 The remaining field equations 45830.4 Charged vacuum metrics 45930.5 A class of radiative Einstein–Maxwell fields (Φ 0 2 ̸= 0) 46030.6 Remarks concerning solutions of the different Petrov types 46130.7 Pure radiation fields 46330.7.1 The field equations 46330.7.2 Generating pure radiation fields from vacuum bychanging P 46430.7.3 Generating pure radiation fields from vacuum bychanging m 46630.7.4 Some special classes of pure radiation fields 46731 Non-diverging solutions (Kundt’s class) 47031.1 Introduction 47031.2 The line element for metrics with Θ + iω = 0 47031.3 The Ricci tensor components 47231.4 The structure of the vacuum and Einstein–Maxwellequation 47331.5 Vacuum solutions 47631.5.1 Solutions of types III and N 47631.5.2 Solutions of types D and II 47831.6 Einstein–Maxwell null fields and pure radiation fields 48031.7 Einstein–Maxwell non-null fields 48131.8 Solutions including a cosmological constant Λ 483