Neutron star masses in $R^2$-gravity

Abstract

We address the issue of the existence of inequivalent definitions of gravitational mass in $R^2$-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 $R^2$-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.

26 pages, 15 figures, pdfLatex, one subsection added and other minor changes, version accepted for publication