Rotating Neutron Stars in F(R) Gravity with Axions

We investigate equilibrium configurations of uniformly rotating neutron stars in $R^2$ gravity with axion scalar field for GM1 equation of state (EoS) for nuclear matter. The mass-radius diagram, mass-central energy density are presented for some frequencies in comparison with static stars. We also compute equatorial and polar radii and moment of inertia for stars. For axion field $\phi$ the coupling in the form $\sim R^2\phi$ is assumed. Several interesting results follow from our consideration. Maximal possible star mass with given EoS increases due to the contribution of coupling term. We discovered the possibility to increase maximal frequency of the rotation in comparison with General Relativity. As a consequence the lower bound on mass of the fast rotating stars decreases. For frequency $f=700$ Hz neutron stars with masses $\sim M_\odot$ can exist for some choice of parameters (in General Relativity for same EoS this limit is around $1.2 M_{\odot}$). Another feature of our solutions is relatively small increase of stars radii for high frequencies in comparison with static case. Thus, eventually the new class of neutron stars in $R^2$ gravity with axions is discovered namely fast rotating compact stars with intermediate masses.