Structure of neutron stars in R-squared gravity

The effects implied for the structure of compact objects by the modification of General Relativity produced by the generalization of the Lagrangian density to the form f(R)=R+\alpha R^2, where R is the Ricci curvature scalar, have been recently explored. It seems likely that this squared-gravity may allow heavier Neutron Stars (NSs) than GR. In addition, these objects can be useful to constrain free parameters of modified-gravity theories. The differences between alternative gravity theories is enhanced in the strong gravitational regime. In this regime, because of the complexity of the field equations, perturbative methods become a good choice to treat the problem. Following previous works in the field, we performed a numerical integration of the structure equations that describe NSs in f(R)-gravity, recovering their mass-radius relations, but focusing on particular features that arise from this approach in the profiles of the NS interior. We show that these profiles run in correlation with the second-order derivative of the analytic approximation to the Equation of State (EoS), which leads to regions where the enclosed mass decreases with the radius in a counter-intuitive way. We reproduce all computations with a simple polytropic EoS to separate zeroth-order modified gravity effects.