Some remarks on the Bel-Robinson Tensor

TL;DR

This paper discusses the physical interpretation of the Bel-Robinson tensor in standard General Relativity, emphasizing its derivation from Bianchi identities and its relation to gravitational energy-momentum in normal coordinates.

Contribution

It clarifies the Bel-Robinson tensor's interpretation without auxiliary structures, linking it to fundamental geometric identities and gravitational energy in GR.

Findings

The Bel-Robinson tensor arises from Bianchi identities.

It is connected to differences in gravitational energy-momentum.

The interpretation is consistent within standard GR without extra assumptions.

Abstract

In this paper we present our point of view on correct physical interpretation of the Bel-Robinson tensor within the framework of the standard General Relativity ({\bf GR}), i.e., within the framework of the {\bf GR} without supplementary elements like arbitrary vector field, distinguished tetrads field or second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the differences of the canonical gravitational energy-momentum calculated in normal coordinates {\bf NC(P)}.