2PN/RM gauge invariance in Brans-Dicke-like scalar-tensor theories

Abstract

In this note we study the 2PN/RM gauge invariance structure of a \textit{Brans-Dicke-like} Scalar-Tensor Theories (STT) without potential. Since the spherical isotropic metric plays an important role in the literature, its 2PN/RM STT version is deduced from the general equations given in \cite{moiCQG11}, by using the invariance structure properties. It is found that the second order Eddington parameter \(\epsilon\) can be written in terms of the usual post-Newtonian parameter \(\gamma\) and \(\beta\) as \( \epsilon=4/3 \gamma^2 + 4/3 \beta - 1/6 \gamma -3/2\)