This review explores the geometry of curved spacetimes equipped with torsionful affinities and reveals the symmetry properties of Witten curvature spinors.
The classical world structures borne by spacetimes endowed with torsionful affinities are reviewed. Subsequently, the definition and symmetry properties of a typical pair of Witten curvature spinors for such spacetimes are exhibited along with a comprehensive two-component spinor transcription of Einstein-Cartan's theory. A full description of the correspondence principle that interrelates Einstein-Cartan's theory and general relativity is likewise presented.
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J. G. Cardoso (2025) studied this question.
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