Conservation of Energy-Momentum in Teleparallel Gravity

Abstract

In a well-known paper arXiv:gr-qc/0003100 V.C. de Andrade, L. C. T. Guillen and J.G. Pereira defined a conserved gauge current, however they stated that: `` This is, we believe the farthest one can go in the direction of a tensorial definition for the energy and momentum of the gravitational field. The lack of local Lorentz covariance can be considered as the teleparallel manifestation of the pseudotensor character of the gravitational energy-momentum density in general relativity....''. Well, we believe that they stopped just less than an inch before giving such a tensorial definition, and furthermore that the resulting energy-momentum tensor has zero trace and can be made symmetric, and together with the energy-momentum tensor of material fields it obeys a natural conservation equation for teleparallel manifolds. Some important consequences are obtained specially in the last section concerning the possibility of explaining the acceleration of the universe expansion without any need of a cosmological constant.