Summary
As it occurs for the Weyl-Levi Civita class of vacuum fields, even the class of stationary, axially symmetric solutions of the general theory of relativity found by Papapetrou may be generalized to the Hermitian theory in a straightforward way.
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Antoci, S. stationary axially symmetric solutions of the Hermitian theory of relativity: Generalization of the papapetrou class of vacuum fields. Lett. Nuovo Cimento 36, 16–20 (1983). https://doi.org/10.1007/BF02754881
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DOI: https://doi.org/10.1007/BF02754881