Distinguishing Black Holes and Superspinars in Spinning Modified Gravity via Generalized Spin Precession Frequency

We compute the generalized spin precession frequency (Ωp) of a test gyroscope in a stationary spacetime, specifically for a Kerr–MOG black hole within the framework of scalar–tensor–vector gravity (STVG), also known as modified gravity (MOG). A comprehensive analysis of the generalized spin frequency was conducted for non-extremal Kerr–MOG black hole, extremal Kerr–MOG black hole, and naked singularity or superspinar, in comparison to non-extremal Kerr black hole, extremal Kerr black hole, and Kerr naked singularity or Kerr superspinar. The generalized spin frequency we derived can be expressed in terms of the black hole mass parameter, the angular momentum parameter, and the MOG parameter. Additionally, we distinguish between non-extremal black hole, extremal black hole, and naked singularity through the computation of the aforementioned precession frequency. Furthermore, we calculate the generalized spin frequency for various angular coordinates, ranging from the polar to the equatorial plane. Lastly, we determine three fundamental epicyclic frequencies, the Keplerian frequency, the radial epicyclic frequency, and the vertical epicyclic frequency, to differentiate these three types of objects. We also compute the periastron frequency and nodal frequency. Utilizing these frequency profiles allows for the distinction of these three compact objects.