Spin Curvatures in General Relativity and Two-Component Gravitons with Arbitrary Sources

TL;DR

This paper reviews spin curvatures in general relativity using the Infeld-van der Waerden formalism and discusses an extension of the two-component graviton theory that emphasizes energy-momentum conservation.

Contribution

It provides an explicit exposition of spinor symmetries in general relativity and reviews a sourceful extension of the two-component graviton theory.

Findings

Explicit spinor symmetry structures in general relativity

Extension of graviton theory to include sources

Connection between graviton theory and energy-momentum conservation

Abstract

We present a short review of the spin curvatures that arise within the framework of one of the Infeld-van der Waerden formalisms for general relativity. All the spinor symmetries borne by the inner structure of general relativity are thus exhibited in an explicit way. The sourceful extension formulated in an earlier work of the two-component theory of gravitons in vacuum is concisely reviewed in connection with the establishment of an important total-symmetry property related to the energy-momentum conservation law of general relativity.