Maximum Forces in Modified Gravity Theories

We investigate the existence and nature of classical maximum force constraints in some gravity theories other than Einstein's. We calculate the maximum force bounds in several of these gravity theories. We are interested in mass-independent maximum force bounds between black holes with touching horizons and find that this mass-independent feature of general relativity in three dimensions is present in Moffat's gravity theory, Brans Dicke theory, and the pure Lovelock theory in which only one term in the lagrangian sum for the general Lovelock lagrangian is retained but not the sum over lower-order terms. Only pure Lovelock theory has this property in higher dimensions when the spatial dimension is equal to three times the Lovelock order contributing the single lagrangian to define the Lovelock lagrangian. we determine whether the maximum force is bigger or smaller than in general relativity. The absence of mass dependence in the maximum force relations may have relevance for the formation of naked singularities.