Bel-Robinson as stress-tensor gradients and their extensions to massive spin (0,1,2)

TL;DR

This paper demonstrates that the Bel-Robinson tensor can be viewed as a conserved double gradient of a system's stress-tensor and extends this concept to massive scalar, vector, and tensor fields, including their higher-spin versions.

Contribution

It introduces a natural extension of the Bel-Robinson tensor from general relativity to massive matter models, including spin (0, 1, 2), via Kaluza-Klein reduction.

Findings

Bel-Robinson tensor is a conserved double gradient of stress-tensor.

Extension to massive scalars, vectors, and tensors is established.

Massive spin (0, 1, 2) Bel-Robinson tensors are constructed.

Abstract

We show that the Bel-Robinson (BR) tensor is - generically, as well as in its original GR setting - an autonomously conserved part of the, manifestly conserved, double gradient of a system's stress-tensor. This suggests its natural extension from GR to matter models, first to (known) massless scalars and vectors, then to massive ones, including tensors. These massive versions are to be expected, given that they arise upon KK reduction of massless D+1 ones. We exhibit the resulting spin (0, 1, 2) "massive" BR.