Abstract
The equivalence of the axisymmetric stationary vacuum gravitational field problem to a 3-dimensional “relativity theory” in the presence of a certain scalar matter field is shown. An invariant classification can be achieved with respect to the algebraic structure of the 3-dimensional trace-free Ricci-tensor. The extension of these results to electrovac spaces is also discussed.
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Perjés, Z. 3-Dimensional “relativity” for axisymmetric stationary space-times. Commun.Math. Phys. 12, 275–282 (1969). https://doi.org/10.1007/BF01667313
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DOI: https://doi.org/10.1007/BF01667313