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

In this note we study the 2PN/RM gauge invariance structure of a $\mathit{\text{Brans-Dicke-like}}$ 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 $ϵ$ 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$