The Newtonian limit of metric gravity theories with quadratic Lagrangians

TL;DR

This paper investigates the Newtonian limit of fourth-order metric gravity theories with quadratic Lagrangians, providing explicit solutions and analyzing their consistency with General Relativity without relying on scalar-tensor equivalences.

Contribution

It offers a detailed analysis of the Newtonian limit in metric fourth-order gravity theories, including explicit solutions and a Green function approach, avoiding scalar-tensor analogies.

Findings

Explicit solutions for various quadratic Lagrangians

Green function method for fourth-order theories

Consistency with General Relativity discussed

Abstract

The Newtonian limit of fourth-order gravity is worked out discussing its viability with respect to the standard results of General Relativity. We investigate the limit in the metric approach which, with respect to the Palatini formulation, has been much less studied in the recent literature, due to the higher-order of the field equations. In addition, we refrain from exploiting the formal equivalence of higher-order theories considering the analogy with specific scalar-tensor theories, i.e. we work in the so-called Jordan frame in order to avoid possible misleading interpretations of the results. Explicit solutions are provided for several different types of Lagrangians containing powers of the Ricci scalar as well as combinations of the other curvature invariants. In particular, we develop the Green function method for fourth-order theories in order to find out solutions. Finally, the consistency of the results with respect to General Relativity is discussed.