Neutron star masses in R2-gravity

We address the issue of the existence of inequivalent definitions of gravitational mass in -gravity. We present several definitions of gravitational mass, and discuss the formal relations between them. We then consider the concrete case of a static and spherically symmetric neutron star, and solve numerically the equations of motion for several values of the free parameter of the model. We compare the features of the mass–radius relations obtained for each definition of gravitational mass, and we comment on their dependence on the free parameter. We then argue that -gravity is a valuable proxy to discuss the existence of inequivalent definitions of gravitational mass in a generic modified gravity theory, and present some comments on the general case.