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Rigidly rotating perfect fluids admitting two Killing vectors ξ (stationarity), η (axial symmetry), and a proper conformal Killing vector K are studied. The three-dimensional Lie algebra [ξ,η]=0, [ξ,K]=a4K, [η,K]=a3K, a32+a42≠0 is considered. It is shown that under these assumptions there are no space-times satisfying Einstein’s field equations.
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Krämer et al. (1991) studied this question.
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