Conserved currents for general teleparallel models

Abstract

The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. In this article a general 3-parameter class of teleparallel models is considered. The field equation turns out to have a form completely similar to the Maxwell field equation $d*\F^a=\T^a$. By applying the Noether procedure, the source 3-form $\T^a$ is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source of the coframe field is interpreted as the total conserved energy-momentum current of the system. A reduction of the conserved current to the Noether current and the Noether charge for the coframe field is provided. An energy-momentum tensor for the coframe field is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in GR. The energy-momentum tensor is calculated for various teleparallel models: the pure Yang-Mills type model, the anti-Yang-Mills type model and the generalized teleparallel equivalent of GR. The latter case can serve as a very close alternative to the GR description of gravity.