The Weak Field Limit of Higher Order Gravity

Abstract

The Higher Order Theories of Gravity - f(R, RαβRαβ) - theory, where R is the Ricci scalar, Rαβ is the Ricci tensor and f is any analytic function - have recently attracted a lot of interest as alternative candidates to explain the observed cosmic acceleration, the flatness of the rotation curves of spiral galaxies and other relevant astrophysical phenomena. It is a crucial point testing these alternative theories in the so called weak field and newtonian limit of a f(R, RαβRαβ) - theory. With this "perturbation technique" it is possible to find spherically symmetric solutions and compare them with the ones of General Relativity. On both approaches we found a modification of General Relativity: the behaviour of gravitational potential presents a modification Yukawa - like in the newtonian case and a massive propagation in the weak field case. When the modification of the theory is removed (i.e. f(R, RαβRαβ) = R, Hilbert - Einstein lagrangian) we find the usual outcomes of General Relativity. Also the Noether symmetries technique has been investigated to find some time independent spherically symmetric solutions.