# Neutron star masses in $R^{2}$-gravity

## TL;DR

This paper investigates different definitions of gravitational mass in $R^{2}$-gravity, analyzing their implications for neutron star models and exploring the broader context of modified gravity theories.

## Contribution

It introduces multiple definitions of gravitational mass in $R^{2}$-gravity$, compares their effects on neutron star properties, and discusses their relevance in generic modified gravity theories.

## Key findings

- Mass-radius relations vary with different mass definitions.
- The free parameter significantly influences the mass-radius curves.
- $R^{2}$-gravity serves as a useful model for studying mass definitions in modified 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.