Weak field reduction in teleparallel coframe gravity. Vacuum case

TL;DR

This paper investigates the weak field approximation in teleparallel coframe gravity, showing that removing a specific term ensures a consistent reduction, viable solutions, and a healthy particle spectrum.

Contribution

It demonstrates that the removal of the pure Yang-Mills term is essential for consistent weak field reduction and physical viability in teleparallel coframe gravity.

Findings

Pure Yang-Mills term removal enables symmetric-antisymmetric reduction.

Ensures existence of Schwarzschild-like solutions.

Prevents ghosts and tachyons in the theory.

Abstract

The teleparallel coframe gravity may be viewed as a generalization of the standard GR. 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 secondary structure. The general Lagrangian, quadratic in the first order derivatives of the coframe field is not unique. It involves three dimensionless free parameters. We consider a weak field approximation of the general coframe teleparallel model. In the linear approximation, the field variable, the coframe, is covariantly reduced to the superposition of the symmetric and antisymmetric field. We require this reduction to be preserved on the levels of the Lagrangian, of the field equations and of the conserved currents. This occurs if and only if the pure Yang - Mills type term is removed from the Lagrangian. The absence of this term is known to be necessary and sufficient for the existence of the viable (Schwarzschild) spherical-symmetric solution. Moreover, the same condition guarantees the absence of ghosts and tachyons in particle content of the theory. The condition above is shown recently to be necessary for a well defined Hamiltonian formulation of the model. Here we derive the same condition in the Lagrangian formulation by means of the weak field reduction.