General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

Testing gravity theories is an important and interesting issue in relativistic astrophysics using astrophysical observations. In recent years, Event horizon telescope collaboration provided valuable data from shadow of supermassive black holes located at the center of the galaxies Milky Way and Meissner 87, which may help to get information about the spacetime around the black holes. In this work, first, we consider rotating black hole solution for charged black hole with the NUT charge in the presence of clouds of strings, and study the event horizon properties of spacetime around rotating twisting and charged black holes in the cloud of strings and quintessential fields. The null geodesics of the spacetime is derived and the shadow case, radius of the shadow of the black and its distortion, due to the effects of the black hole spin, also analyzed. It is obtained that gravitational effects of black hole charge and quintessential field compensate each other and the rotating black hole’s shadow can be circular. We obtain constraints on charge and spin parameters of supermassive black holes Sgr $$\hbox {A}^*$$A ∗ and $$\hbox {M87}^*$$M87 ∗ using observational data from their shadow (size and observational angle) for various values of the NUT charge, cloud of strings and quintessential field parameters. Moreover, we also investigate gravitational capture cross-section for electromagnetic waves and emission rate of the black hole radiation energy through Hawking evaporation.

Throughout this work, we explored the dynamics of test particles with magnetic dipole moment around magnetized rotating Kerr black holes in scalar–vector–tensor gravity theory (STVG), known as modified gravity theory (MOG). We assume that the black hole is immersed in external asymptotically uniform magnetic fields. We derive effective potential for circular orbits of the magnetized particles, taking into account both the magnetic and STVG interactions. We study profiles of the position of the innermost stable circular orbits (ISCOs) of the magnetized particles. We show that the MOG interaction is essentially, and the magnetic interaction enhances its effects on the ISCO radius and the angular momentum at ISCO. Also, we consider collisional cases of magnetized particles and the maximum and minimum limits of angular momentum that ensure the particle colliding near the horizon. Finally, we analyze the center-of-mass energy of colliding magnetized particles near the black hole horizon.