On irreducible partials of Ricci tensor traceless part in finite space-time region in GR

TL;DR

This paper investigates the irreducible part of the Ricci tensor in general relativity, expressing it through bivector fields, deriving field equations from Bianchi identities, and revealing a three-parameter local symmetry group akin to Yang-Mills theory.

Contribution

It introduces a novel expansion of the Ricci tensor's traceless part into bivector eigenfunctions and analyzes the resulting field equations, uncovering a Yang-Mills-like symmetry group.

Findings

The Ricci tensor's traceless part can be expanded into bivector eigenfunctions.

Field equations derived from Bianchi identities suggest a three-parameter symmetry group.

The symmetry group resembles a Yang-Mills gauge group.

Abstract

Riemann tensor irreducible part $E_{iklm} = {1/2} (g_{il}S_{km} + g_{km}S_{il} - g_{im}S_{kl} - g_{kl}S_{im})$ constructed from metric tensor $g_{ik}$ and traceless part of Ricci tensor $S_{ik} = R_{ik} - {1/4} g_{ik} R$ is expanded into bilinear combinations of bivectorial fields being eigenfunctions of $E$. Field equations for the bivectors induced by Bianchi identities are studied and it is shown that in general case it will be 3-parametric local symmetry group Yang-Mills field.