Post-Newtonian approximation in higher-order metric theories of gravity

The Post-Newtonian limit of a fourth-order metric theory of gravity is discussed, based on the most general quadratic Lagrangian. This approach involves the use of the perturbation expansion of the metric tensor, extended up to the fourth-order and expressed in terms of three gravitational potentials. The analysis concerns the search and the resolution, where possible, of systems of coupled fourth-order differential equations, obtained by varying the conditions placed on the coupling constants appearing in the Lagrangian. The solutions are computed using the Green’s function method. Finally, the gravitational potentials thus obtained are compared with the Newtonian one derived in General Relativity in the weak-field and low-veocity limit.