Post-Newtonian limit of generalized scalar-torsion theories of gravity
Kai Flathmann, Manuel Hohmann
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 $L(T,X,Y,\ensuremath{\phi})$ of the torsion scalar $T$ and scalar quantities $X$ and $Y$ built from the dynamical scalar field $\ensuremath{\phi}$. We restrict the analysis to a massless scalar field in order to use the parametrized 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 nonvanishing parameters are $\ensuremath{\gamma}$ and $\ensuremath{\beta}$. For a particular choice of the function $L(T,X,Y,\ensuremath{\phi})$ the theory cannot be distinguished from general relativity in its post-Newtonian approximation.