On the Weak-Field Approximation in Generalized Scalar-Tensor Gravities

In the paper published in Phys. Lett. A245} (1998) 31, Barros and Romero demonstrated that, in the weak-field approximation, solutions to the Brans-Dicke equations are related to the solutions of General Relativity for the same matter distributions. In the present work, we enphasize this result and we extend it to for generalized scalar-tensor theories in which the parameter $\omega$ is no longer a constant but an arbitrary function of the (gravitational) scalar field.