Orbital and epicyclic frequencies around neutron and strange stars in $R^2$ gravity

Abstract: According to various models, the orbital and the epicyclic frequencies of particles moving on a circular orbit around compact objects are related to the quasi-periodic oscillations observed in the X-ray flux of some pulsars or black hole candidates. It is expected that they originate from the inner edge of the accretion discs, deep into the gravitational field of the compact objects. Considering the planned new generation X-ray timing observatories with large collective areas, the quasi-periodic oscillations might be an excellent tool for testing gravity in strong field regime and respectively alternative gravitational theories. We examine the orbital and the epicyclic frequencies of a particle moving on a circular orbit around neutron or strange stars in $R^2$ gravity. The case of slow rotation is considered too. The $R^2$ gravity results are compared to the General Relativistic case. We comment the deviations from General Relativity, as well as the deviations due to rotation in both theories.