We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general solutions which { are perturbed Schwarzschild metric and viable for solar system. Our results for large scale contains a logarithmic term with a coefficient producing a repulsive gravity force which is in agreement with the positive acceleration of the universe.
Categories: physics.gen-ph