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In this work, we have presented a detailed analysis of the event horizon of regular black holes (BHs) in modified gravity known as MOG, the so-called regular MOG BH. The motion of neutral particles around the BH has also been explored. The test particle motion study shows that the positive (negative) values of the MOG parameter mimic the spin of a rotating Kerr BH, providing the same values for the innermost stable pro-grade (retrograde) orbits of the particles in the range of the spin parameter a/M∈(−0.4125,0.6946). The efficiency of energy release from the accretion disk by the Novikov–Thorne model has been calculated, and the efficiency was shown to be linearly proportional to the increase of the MOG parameter α. Moreover, we have developed a new methodology to test gravity theories in strong-field regimes using precision data from twin-peaked quasiperiodic oscillations (QPOs) of objects calculating possible values of upper and lower frequencies. However, it is obtained that the positive MOG parameter can not mimic the spin of Kerr BHs in terms of the same QPO frequencies. We have provided possible ranges for upper and lower frequencies of twin-peak QPOs with the ratio of the upper and lower frequencies of 3:2 around regular MOG BHs in the different models. Moreover, as an example, we provide detailed numerical analysis of the QPO of GRS 1915+105 with the frequencies νU=168±5Hz and νL=113±3Hz. It is shown that the central BH of the QPO object can be a regular MOG BH when the value of the parameter is α=0.2844−0.1317+0.0074 and shines in the orbits located at the distance r/M=7.6322−0.0826+0.0768 from the central BH. It is also shown that the orbits where QPOs shine are located near the innermost stable circular orbit (ISCO) of the test particle. The correlation between the radii of ISCO and the QPO orbits is found, and it can be used as a new theoretical way to determine ISCO radius through observational data from the QPOs around various compact objects.
Rayimbaev et al. (Thu,) studied this question.