Modified Gravity and Relativistic Stars ^†

We construct nonperturbative models of compact stars in f(R) = R + αR² -gravity and scalar-tensor gravity. For α > 0 the shooting method of solution gives that there is unique value of curvature at the center of star at which solution has required Schwarzschild asymptotic. For distant observer the gravitational mass of star increases negligibly for realistic values of α with increasing α. One can say that increasing of mass occurs by “gravitational sphere” outside the star with some “effective mass”. For α < 0 we have no rigid condition on R at center of star but there are no realistic solutions. The contribution to mass from gravitational field grows infinitely with distance.