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

TL;DR

This paper investigates the gauge invariance of second post-Newtonian/relativistic motion in Brans-Dicke-like scalar-tensor theories, deriving relations between Eddington parameters and standard post-Newtonian parameters.

Contribution

It derives the 2PN/RM gauge invariance structure for Brans-Dicke-like theories and expresses the second order Eddington parameter in terms of PPN parameters.

Findings

The second order Eddington parameter psilon is expressed in terms of mma and eta.

The 2PN/RM gauge invariance structure is characterized for these theories.

The spherical isotropic metric version is deduced from general equations.

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$