On the linear and weak-field limits of scalar-tensor theories of gravity

TL;DR

This paper investigates the linear and weak-field limits of scalar-tensor gravity theories, analyzing deviations from Newtonian gravity and scalarization effects in extended objects within these regimes.

Contribution

It provides a detailed analysis of the linear approximation and weak-field behavior of scalar-tensor theories in different formalisms, highlighting conditions for deviations from Newtonian gravity.

Findings

Conditions for deviations from Newton's law identified

Scalarization effects in extended objects analyzed

Weak-field limit behavior characterized

Abstract

The linear approximation of scalar-tensor theories of gravity is obtained in the physical (Jordan) frame under the 4+0 (covariant) and 3+1 formalisms. Then the weak-field limit is analyzed and the conditions leading to significant deviations of the $1/r^{2}$ Newton's law of gravitation are discussed. Finally, the scalarization effects induced by these theories in extended objects are confronted within the weak-field limit.