Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories

TL;DR

This paper analyzes the post-Newtonian limit of scalar-torsion gravity theories, extending scalar-curvature theories, and determines how these theories compare to general relativity in weak-field conditions.

Contribution

It introduces a scalar-torsion gravity framework analogous to scalar-curvature theories and computes its post-Newtonian parameters for massive and massless scalar fields.

Findings

Effective gravitational constant depends on distance in massive case

Post-Newtonian parameter gamma varies with scalar field mass

Theory reduces to general relativity for minimally coupled scalar fields

Abstract

We consider a recently proposed class of extended teleparallel theories of gravity, which entail a scalar field which is non-minimally 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 a massless scalar field. In the massive case, we determine the effective gravitational constant and the post-Newtonian parameter $\gamma$, 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 $\gamma$ and $\beta$ 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.