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21.1 Einstein–Maxwell fields 325Table 21.1.Stationary axisymmetric Einstein–Maxwell fieldsOnly the parameters marked by a cross (×) are different from zero in thecorresponding solution.m l a b e g Λ References× × × × × × × Debever (1971), Plebańskiand Demiański(1976)× × × × × × Kinnersley (1969b)× × × × × × Plebański(1975)× × × × × Demiańskiand Newman (1966)× × × × × ⎫⎬× × × × × Carter (1968a, 1968b)⎭× × × ×× × × Brill (1964)× × × Newman et al. (1965)× × Bertotti(1959), Robinson (1959)× × Reissner (1916), Nordström (1918)This is the gravitational field generated by two uniformly acceleratedcharged mass points, the parameter b being the acceleration parameter(Kinnersley and Walker 1970, Walker and Kinnersley 1972, PlebańskiandDemiański1976). Note that b may be put equal to zero in (21.22) butnot in (21.20), because the transformation (21.21) involves b explicitly.Putting b = 0 in (21.22) we get the Reissner–Nordström solution in termsof the retarded time coordinate u (cp. (15.17) and Table 15.1). The singularitybetween the sources is removed in a more general metric (Ernst1976), which contains an additional parameter describing an electric fieldwhich causes the uniform acceleration of the charges.A particular limit of the general metric (21.11) can be considered asa superposition of the Schwarzschild and Bertotti–Robinson solutions(Halilsoy 1993a).In Table 21.1, taken from Plebańskiand Demiański(1976), special casesof the metric (21.11) which had been given earlier in the literature arelisted.21.1.3 The Kerr–Newman solutionThe Kerr–Newman solution is a special case of the type D solutions discussedin §21.1.2. Newman et al. (1965) found it by applying a complexsubstitution (see §21.1.4) to the preferred complex null tetrad of the Kerr