The Seven Classes of the Einstein Equations

TL;DR

This paper revisits a geometric classification of Einstein equations based on tensor representation theory, providing a detailed analysis of the different classes within this framework.

Contribution

It offers a deeper investigation into the classes of Einstein equations using classical tensor decomposition methods.

Findings

Detailed classification of Einstein equations into seven classes

Enhanced understanding of tensor decomposition in geometric contexts

Potential implications for solving Einstein equations more systematically

Abstract

In current paper we refer to the geometrical classification of the Einstein equations which has been developed by one of the authors of this paper. This classification was based on the classical theory for decomposition of the tensor product of representations into irreducible components, which is studied in the elementary representation theory for orthogonal groups. We return to this result for more detailed investigation of classes of the Einstein equations.