Weak field reduction in teleparallel coframe gravity: Vacuum case

Itin Y.

The teleparallel coframe gravity may be viewed as a generalization of the standardGR. A coframe (a field of four independent 1-forms) is considered, in this approach,to be a basic dynamical variable. The metric tensor is treated as a secondarystructure. The general Lagrangian, quadratic in the first order derivatives of thecoframe field is not unique. It involves three dimensionless free parameters. Weconsider a weak field approximation of the general coframe teleparallel model. Inthe linear approximation, the field variable, the coframe, is covariantly reduced tothe superposition of the symmetric and antisymmetric field. We require this reductionto be preserved on the levels of the Lagrangian, of the field equations, and ofthe conserved currents. This occurs if and only if the pure Yang-Mills-type term isremoved from the Lagrangian. The absence of this term is known to be necessaryand sufficient for the existence of the viable (Schwarzschild) spherical-symmetricsolution. Moreover, the same condition guarantees the absence of ghosts and tachyonsin particle content of the theory. The condition above is shown recently tobe necessary for a well-defined Hamiltonian formulation of the model. Here wederive the same condition in the Lagrangian formulation by means of the weak fieldreduction.