Pressure effects in the weak-field limit of f (R)=R+αR2 gravity

We investigate the linear regime of f(R)=R+αR2 gravity for static, spherically symmetric and asymptotically flat configurations of matter. We show that, in vacuum and deep inside the range of the extra scalar degree of freedom, the post-Newtonian parameter γ is not equal to 1/2, as established in the literature, but it assumes larger values depending on the pressure of the star. We provide an explicit expression for γ in terms of the mass, of the integrated pressure of the star and of the ratio between the star's radius and the range of the extra degree of freedom. We corroborate our results by providing numerical solutions for the case of a neutron star.