Post-Newtonian limit of generalized scalar-torsion theories of gravity

TL;DR

This paper derives the post-Newtonian limit of a broad class of teleparallel scalar-torsion gravity theories, identifying conditions under which they match General Relativity or exhibit distinct gravitational parameters.

Contribution

It provides the first detailed post-Newtonian analysis of generalized scalar-torsion theories, revealing their parameter space and conditions for equivalence with GR.

Findings

Certain theories are indistinguishable from GR in the post-Newtonian regime.

Identified fully conservative subclasses with only gamma and beta parameters.

Some models predict deviations detectable by precision gravitational tests.

Abstract

In this article we derive the post-Newtonian limit of a class of teleparallel theories of gravity, where the action is a free function $L(T,X,Y,\phi)$ of the Torsion scalar $T$ and scalar quantities $X$ and $Y$ built from the dynamical scalar field $\phi$. We restrict the analysis to a massless scalar field in order to use the parameterized post-Newtonian formalism without modifications, such as introducing an effective gravitational constant which depends on the distance between the interacting masses. In particular the results show a class of fully-conservative theories of gravity, where the only non-vanishing parameters are $\gamma$ and $\beta$. For a particular choice of the function $L(T,X,Y,\phi)$ the theory cannot be distinguished from General Relativity in its post-Newtonian approximation.