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

TL;DR

This paper investigates how orbital and epicyclic frequencies around neutron and strange stars differ in $R^2$ gravity compared to General Relativity, with implications for testing gravity using X-ray observations.

Contribution

It provides a comparative analysis of orbital frequencies in $R^2$ gravity and General Relativity, including effects of slow rotation, to aid in testing gravity theories.

Findings

Deviations from General Relativity are identified in orbital frequencies.

Rotation effects cause additional deviations in frequencies.

Results suggest potential for observational tests of $R^2$ 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.