Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
E. D. Emtsova, Manuel Hohmann
Abstract
We consider a recently proposed class of extended teleparallel theories of gravity, which entail a scalar field which is nonminimally coupled to the torsion of a flat, metric-compatible connection. This class of scalar-torsion theories of gravity is constructed in analogy to and as a direct extension of the well-studied class of scalar-curvature gravity theories, and has various common features, such as the conformal frame freedom. For this class we determine the parametrized post-Newtonian limit, both for a massive and for a massless scalar field. In the massive case, we determine the effective gravitational constant and the post-Newtonian parameter $\ensuremath{\gamma}$, both of which depend on the distance between the gravitating and test masses. In the massless case, we calculate the full set of parameters and find that only $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ potentially deviate from their general relativity values. In particular, we find that for a minimally coupled scalar field, the theory becomes indistinguishable from general relativity at this level of the post-Newtonian approximation.