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The Einstein-Maxwell field equations in the presence of one Killing vector are shown to possess covariance under an eight-parameter group of linear substitutions in the field variables. This internal symmetry group is isomorphic to SU(2,1). Three of the degrees of freedom correspond to gage transformations, but the remaining ones allow us to generate a five-parameter family of solutions given a single solution.
William Kinnersley (Tue,) studied this question.