Some remarks on the Bel-Robinson tensor and gravitational radiation

TL;DR

This paper examines the Bel-Robinson tensor's behavior in gravitational radiation zones, compares it with standard power emission formulas, and discusses covariant descriptions of gravitational radiation.

Contribution

It provides an asymptotic form of the Bel-Robinson tensor in radiation zones and explores its potential for a covariant description of gravitational waves.

Findings

Derived the asymptotic form of the Bel-Robinson tensor in radiation zones

Compared the tensor-based approach with standard gravitational power formulas

Discussed the covariant formulation of gravitational radiation

Abstract

The asymptotic form of the Bel-Robinson tensor in the gravitational radiation-zone is obtained in terms of the mass quadrupole of the source. A comparison is made with the standard formula for the gravitational power emission. The problem of a fully covariant description of gravitational radiation in terms of this tensor is discussed with some detail.