On the weak field approximation of Brans-Dicke theory of gravity

TL;DR

This paper demonstrates a straightforward method to derive Brans-Dicke gravity solutions from Einstein's solutions in the weak field limit, simplifying the analysis of alternative gravity theories.

Contribution

A simple linearized method is developed to relate Brans-Dicke solutions to Einstein solutions, facilitating easier analysis of scalar-tensor gravity theories.

Findings

Brans-Dicke solutions can be directly obtained from Einstein solutions in the weak field limit.

The method simplifies the process of analyzing scalar-tensor theories of gravity.

Examples from literature are discussed to illustrate the approach.

Abstract

It is shown that in the weak field approximation solutions of Brans-Dicke equations are simply related to the solutions of General Relativity equations for the same matter distribution. A simple method is developed which permits to obtain Brans-Dicke solutions from Einstein solutions when both theories are considered in their linearized forms. To illustrate the method some examples found in the literature are discussed.