Bondi-Sachs energy-momentum and the energy of gravitational radiation

TL;DR

This paper develops a new expression for gravitational energy-momentum in Bondi-Sachs space-time within TEGR, incorporating the energy of gravitational radiation through functions describing radiating degrees of freedom.

Contribution

It introduces a novel term in the energy-momentum expression that accounts for gravitational radiation, extending the standard Bondi-Sachs energy-momentum in TEGR.

Findings

New term in energy-momentum accounts for gravitational radiation

Standard energy expression plus radiation energy term

Interpretation of functions c and d as radiating degrees of freedom

Abstract

We construct the gravitational energy-momentum of the Bondi-Sachs space-time, in the famework of the teleparallel equivalent of general relativity (TEGR). The Bondi-Sachs line element describes gravitational radiation in the asymptotic region of the space-time, and is determined by the mass aspect and by two functions, $c$ and $d$, that yield the news functions, which are interpreted as the radiating degrees of freedom of the gravitational field. The standard expression for the Bondi-Sachs energy-momentum is constructed in terms of the mass aspect only. The expression that we obtain in the context of the TEGR is given by the standard expression, which represents the gravitational energy of the source, plus a new term that is determined by the two functions $c$ and $d$. We interpret this new term as the energy of gravitational radiation.