Energy of Gravitational Radiation and the Background Energy of the Space-Time

TL;DR

This paper explores the energy of gravitational radiation within the Bondi-Sachs framework using TEGR, suggesting that background gravitational radiation is inherent in space-time and may relate to noise in gravitational wave detectors.

Contribution

It provides a new expression for gravitational energy in TEGR that is independent of distance and depends on news functions, analyzing its physical and mathematical properties in axial symmetry.

Findings

Energy expression is independent of radial distance.

Gravitational radiation persists in the background structure of space-time.

Background gravitational radiation may be linked to detector noise.

Abstract

We address the issue of gravitational radiation in the context of the Bondi-Sachs space-time, and consider the expression for the gravitational energy of the radiation obtained in the realm of the teleparallel equivalent of general relativity (TEGR). This expression is independent of the radial distance (i.e., of powers of $1/r$) and depends exclusively on the functions $c(u,\theta,\phi)$ and $d(u,\theta,\phi)$, which yield the news functions ($u$ is the retarded time, $u=t-r$). We investigate the mathematical and physical features of this energy expression in the simpler framework of axial symmetry. Once a burst of gravitational radiation takes place in a self gravitating system, that leads to a loss of the Bondi mass, gravitational radiation is emitted throughout the whole space-time. The existence and presence of this radiation in the background structure of the space-time is consistent with the analysis developed by Papapetrou, and Hallidy and Janis, who found no proof that a gravitational system that emits a burst of gravitational radiation is preceded and followed by two stationary gravitational field configurations, namely, it seems that it is impossible for a gravitational system, which is initially stationary, to return to a stationary state after emitting a burst of axially symmetric gravitational radiation, in which case the space-time is not even asymptotically stationary. Therefore, it is plausible that the gravitational energy of radiation is present in the background structure of the space-time, and this is the energy predicted in the TEGR. This analysis lead us to conjecture that the noise detected in the large terrestrial gravitational wave observatories is intrinsically related to the background gravitational radiation.