Abstract
The method of reduction of a connection form from a principal fibre-bundle to a sub-bundle is studied by considering the null tetrad formalism in space-time and discussing in detail the resulting Generalized Maurer-Cartan Structural Equations.
Vacuum space-times satisfying Einstein field equations and admitting the vanishing of the induced curvature form in the reduced bundle are investigated. It is shown that these hypotheses imply the existence of a field surface orthogonal to a real null geodesic vector of the tetrad field.
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This work was carried out under the auspices of the National Group of Mathematical Physics of CNR.
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Cianci, R. On generalized torsion two-forms in general relativity: a result of null tetrad formalism. Lett Math Phys 5, 481–487 (1981). https://doi.org/10.1007/BF00408129
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DOI: https://doi.org/10.1007/BF00408129