Action growth for black holes in modified gravity

The general form of the action growth for a large class of static black hole solutions in modified gravity which includes F(R)-gravity models is computed. The cases of black hole solutions with nonconstant Ricci scalar are also considered, generalizing the results previously found and valid only for black holes with constant Ricci scalar. An argument is put forward to provide a physical interpretation of the results, which seem tightly connected with the generalized second law of black hole thermodynamics.