Obtaining the Weyl tensor from the Bel-Robinson tensor

TL;DR

This paper develops an algebraic framework to derive the Weyl tensor from the Bel-Robinson tensor, providing a systematic method for tensor reconstruction in general relativity.

Contribution

It introduces a canonical form for algebraic types and an algorithm to determine the Weyl tensor from the Bel-Robinson tensor, advancing tensor analysis in gravitational theory.

Findings

Canonical forms for algebraic types are established.

An explicit algorithm for tensor reconstruction is provided.

The approach enhances understanding of the Bel-Robinson and Weyl tensors relationship.

Abstract

The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor from the Bel-Robinson tensor is presented.