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

TL;DR

The paper surveys curvature spinors within the $Infeld$-$van$-$der$-$Waerden$ two-component spinor formalism for general relativity, highlighting how curvature data splits into gravitational and electromagnetic parts via spinors such as $X_{ABCD}$ and $\Psi_{ABCD}$ and how the Weyl gauge group governs their transformations. It develops a sourcelike graviton theory, proving a total-symmetry property tied to covariant energy-momentum conservation and forms the coupled graviton-field equations. A calculational framework based on $\Delta$-derivatives, the world-spin invariant operator $\square$, and the $\mathbf{G}$-pair curvature spinors expresses the full curvature content and its coupling to matter. The work discusses vacuum and conformally flat limits, counts degrees of freedom of the curvature spinors, and outlines extensions to torsionful spacetimes, offering a structured route to gravitons and their interactions in a spinor GR setting.

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.