Static Bondi energy in the teleparallel equivalent of general relativity

摘要

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 pseudotensors in the static case. In the nonstatic case, Bondi defines the 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 a three-dimensional spacelike hypersurface, whose boundary is far from the source.