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

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,ϕ) of the Torsion scalar T and scalar quantities X and Y built from the dynamical scalar field ϕ. 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 γ and β. For a particular choice of the function L(T,X,Y,ϕ) the theory cannot be distinguished from General Relativity in its post-Newtonian approximation.