Static Bondi Energy in the Teleparallel Equivalent of General Relativity

TL;DR

This paper calculates Bondi's gravitational energy in the teleparallel equivalent of general relativity (TEGR), providing a new expression for energy in radiating spacetimes and relating it to Moller’s energy.

Contribution

It expresses Bondi's radiating metric in asymptotically spherical coordinates within TEGR and derives a novel energy expression applicable to static and nonstatic cases.

Findings

Derived Bondi energy in TEGR framework.

Established relationship with Moller’s energy.

Applicable to both static and radiating solutions.

Abstract

We consider Bondi's radiating metric in the context of the teleparallel equivalent of general relativity (TEGR). This metric describes the asymptotic form of a radiating solution of Einstein's equations. The total gravitational energy for this solution can be calculated by means of pseudo-tensors in the static case. In the nonstatic case, Bondi defines the {\it mass aspect} $m(u)$, which describes the mass of an isolated system. In this paper we express Bondi's solution in asymptotically spherical 3+1 coordinates, not in radiation coordinates, and obtain Bondi's energy in the static limit by means of the expression for the gravitational energy in the framework of the TEGR. We can either obtain the total energy or the energy inside a large (but finite) portion of the three-dimensional spacelike hypersurface, whose boundary is far away from the source. The relationship of the present energy expression with Moller's energy is established.