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On the selection of triads in the teleparallel geometry and Bondi's radiating metric

K. H. Castello-Branco·J. W. Maluf
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Abstract

A consistent Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) requires the theory to be invariant under the global SO(3) symmetry group, which acts on orthonormal triads in three-dimensional spacelike hypersurfaces. In the TEGR it is possible to make definite statements about the energy of the gravitational field. In this geometrical framework two sets of triads related by a local SO(3) transformation yield different descriptions of the gravitational energy. Here we consider the problem of assigning a unique set of triads to the metric tensor restricted to the three-dimensional hypersurface. The analysis is carried out in the context of Bondi's radiating metric. A simple and original expression for Bondi's news function is obtained, which allows us to carry out numerical calculations and verify that a triad with a specific asymptotic behaviour yields the minimum gravitational energy for a fixed space volume containing the radiating source. This result supports the conjecture that the requirement of a minimum gravitational energy for a given space volume singles out uniquely the correct set of orthonormal triads.

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K. H. Castello-Branco, J. W. Maluf. 2000-03-01. On the selection of triads in the teleparallel geometry and Bondi's radiating metric. https://arxiv.org/abs/gr-qc/0003001

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