Abstract
In the present paper we investigate self-consistently slowly rotating neutron and strange stars in R-squared gravity with Lagrangian f(R) = R + aR2, where a is a parameter. For this purpose we first derive the equations describing the structure of the slowly rotating compact stars in f(R)-gravity and then simultaneously solve numerically the exterior and the interior problem. The structure of the slowly rotating neutron stars is studied for two different hadronic equations of state and a strange matter equation of state. The moment of inertia and its dependence on the stellar mass and the R-squared gravity parameter a is also examined in details. The numerical results show that the neutron star moment of inertia can be up to 30% larger compared to the corresponding general relativistic models. This is much higher than the change in the maximum mass induced by R-squared gravity and is beyond the EOS uncertainty. In this way the future observations of the moment of inertia of compact stars could allow us to distinguish between general relativity and f(R) gravity, and more generally to test the strong field regime of gravity.