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

Key Points

• The review presents the classical structures of curved spacetimes endowed with torsionful affinities, shedding light on their unique geometrical properties.
• It reveals the symmetry properties of Witten curvature spinors, underscoring their role in the context of torsionful spacetimes and spinor fields.
• A two-component spinor transcription of Einstein-Cartan's theory is discussed, demonstrating its compatibility with the geometrical framework outlined.
• The correspondence principle connecting Einstein-Cartan's theory with general relativity is elaborated, showing the foundational links between these theories.