Conserved currents for general teleparallel models

TL;DR

This paper develops a general framework for conserved currents in teleparallel gravity models, defining an energy-momentum tensor that is conserved and covariant, offering an alternative to General Relativity.

Contribution

It introduces a 3-parameter class of teleparallel models with a conserved energy-momentum tensor, extending the understanding of gravitational energy in alternative geometries.

Findings

Conserved energy-momentum current is established for teleparallel models.

The energy-momentum tensor is covariant and conserved in these models.

Generalized teleparallel gravity can serve as an alternative to GR.

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.