Energy-momentum current for coframe gravity

The obstruction for the existence of an energy-momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. This must not be valid for alternative geometrical structures. A teleparallel manifold is defined as a parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields related by global Lorentz, i.e. SO(1, 3) transformations. In this paper a general free parametric class of teleparallel models is considered. It includes a 1-parameter subclass of viable models with the Schwarzschild coframe solution. A new form of the coframe field equation is derived from the general teleparallel Lagrangian by introducing the notion of a 3-parameter conjugate field strength Fa. The field equation turns out to have a form completely similar to the Maxwell field equation d * Fa = Ta. By applying the Noether procedure, the source 3-form Ta is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source Ta of the coframe field is interpreted as the total conserved energy-momentum current. The energy-momentum tensor for the coframe is defined. The total energy-momentum current of a system of a coframe and a material field is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) fields is possible in principle, unlike in the standard GR. For special values of parameters, when the GR is reinstated, the energy-momentum tensor gives up the invariant sense, i.e. becomes a pseudo-tensor. Thus even a small-parametric change of GR turns it into a well-defined Lagrangian theory