Distinguishing regular and singular black holes in modified gravity

This paper is devoted to investigate the possible ways of distinguishing regular and singular black holes (BHs) in modified gravity (MOG) called regular MOG (RMOG) and Schwarzschild MOG (SMOG) BHs through observational data from twin peak quasiperiodic oscillations (QPOs) which are generated by test particles in stable orbits around the BHs. The presence of MOG field causes to sufficiently the mpeak in effective potential for a radial motion of test particles. The effect of MOG parameter on specific angular momentum and energy has also studied. As a main part of the paper, we focus on investigations of QPOs around SMOG and RMOG BHs in RP model and the relations of upper and lower frequencies of twin peak QPOs in SMOG and RMOG BH models together with extreme rotating Kerr and Schwarzschild BH. Moreover, possible parameters for the central BHs of the objects GRS J1915 + 105 and XTE 1550 – 564 have also obtained numerically in the relativistic precession (RP) model. Finally, we provide comparisons of the innermost stable circular orbit (ISCO) and the orbits where twin peak QPOs with the ratio 3:2 taken place and show that QPOs can not be generated at/inside ISCO and there is a correlation between the radius of ISCO and QPO orbits.