Geometry of Curved Spacetimes Equipped with Torsionful Affinities and Einstein-Cartan's Theory in Two-Component Spinor Form

Abstract: 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.