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

J. G. Cardoso

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.

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.
Paper Structure (5 sections, 100 equations)

This paper contains 5 sections, 100 equations.

Table of Contents

  1. Introduction
  2. Torsional Geometry and Einstein-Cartan's Theory
  3. Einstein-Cartan's Theory in Spinor Form
  4. The Correspondence Principle
  5. Concluding Remarks