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This paper is devoted to study weak gravitational lensing properties around black hole surrounded plasma medium in modified gravity (MOG). We have investigated the effects of the MOG-parametr and plasma medium on the deflection angle and total magnification of the images. we have presented the comparisons of the effects of the uniform plasma, singular isothermal sphere and non-singular isothermal sphere. We have also shown that the uniform plasma effects significantly stronger than the other models of plasma medium.Through the studies of the total magnifications of images of a remote source we have shown that the effects of the MOG parameter and plasma medium are similar and the increase of the MOG parameter and plasma frequency cause to increase the total magnification. Moreover, we have explored and analyzed how the MOG effects can reflect the plasma medium providing the same values of the total magnification of images.

In this paper, we investigate circular orbits for test particles around the Schwarzschild–de Sitter (dS) black hole surrounded by perfect fluid dark matter. We determine the region of circular orbits bounded by innermost and outermost stable circular orbits. We show that the impact of the perfect fluid dark matter shrinks the region where circular orbits can exist as the values of both innermost and outermost stable circular orbits decrease. We find that for specific lower and upper values of the dark matter parameter there exist double matching values for inner and outermost stable circular orbits. It turns out that the gravitational attraction due to the dark matter contribution dominates over cosmological repulsion. This gives rise to a remarkable result in the Schwarzschild–de Sitter black hole surrounded by dark matter field in contrast to the Schwarzschild–de Sitter metric. Finally, we study epicyclic motion and its frequencies with their applications to twin peak quasi-periodic oscillations (QPOs) for various models. We find the corresponding values of the black hole parameters which could best fit and explain the observed twin peak QPO object GRS 1915+109 from microquasars.

The present work is devoted to the study of the dynamics of charged particles around Simpson–Visser black holes (with the length parameter l ≤ 2) and wormholes ( l > 2 ) immersed in an external asymptotically uniform magnetic field. To do this, first, we solve the Maxwell equation for 4-potentials of the electromagnetic field and show that the difference between the numerical solution and Wald’s solution is small enough to neglect it, which may allow us to use the solution obtained by Wald. We also study fundamental frequencies of in the vertical and radial oscillations of charged particles around circular stable orbits around the magnetized black hole. The effects of the magnetic interaction and length parameters on the fundamental frequencies. We investigate the quasiperiodic oscillations (QPOs) around the black hole in relativistic precession and epicyclic resonance models. It is also shown that the combined effects of magnetic interaction for negatively charged particles and length parameters can mimic the spacetime effects of the Schwarzschild black hole compensating for their effects, as well as the spin of rotating Kerr black holes. The distance between an orbit where a QPO is generated with the ratio of upper and lower frequencies 3: 2 and innermost stable circular orbits is also studied. It is found that the QPO orbits are very close to ISCO in the RP model at l < 2 . This implies that the obtained result helps to determine the ISCO around black holes. We also study the applications of observed QPOs around stellar-mass black holes in microquasars and supermassive black holes.

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*.

We study the motion of charged particles around Schwarzschild black holes immersed in external (i) asymptotically uniform, (ii) dipolar, and (iii) parabolic-like magnetic fields. The effect of the different magnetic-field configurations on the position of innermost stable circular orbits (ISCOs) for test-charged particles is analyzed. Furthermore, we investigated frequencies of radial and vertical oscillations of the charged particles along their stable circular orbits together with the Keplerian one. As an astrophysical application, we explore quasiperiodic oscillations (QPOs) observed in microquasars sourced by black hole candidates in the frame of the relativistic precession (RP) model. In order to obtain constraints on the values of the magnetic parameter and black hole mass for the microquasars GRO J1655-40 and GRS 1915-105, we use the method so-called χ 2 in the Bayesian approach. Also, we get constraints on the magnetic field around the black hole in the microquasars by treating electrons and protons as oscillating test-charged particles in the accretion disc. Our performed analyses show that the masses of black hole candidates in the above-mentioned objects and magnetic parameters are different for the uniform and dipolar magnetic field configurations. However, no constraints on the magnetic field and black hole masses are obtained in the case of a parabolic magnetic field configuration. The obtained results on the black hole masses are compared with the measurements in independent astrophysical observations of these black hole masses.

We consider electromagnetic fields and charged particle dynamics around non-singular black holes in conformal gravity immersed in an external, asymptotically uniform magnetic field. First, we obtain analytic solutions of the electromagnetic field equation around rotating non-singular black holes in conformal gravity. We show that the radial components of the electric and magnetic fields increase with the increase of the parameters L and N of the black hole solution. Second, we study the dynamics of charged particles. We show that the increase of the values of the parameters L and N and of magnetic field causes a decrease in the radius of the innermost stable circular orbits (ISCO) and the magnetic coupling parameter can mimic the effect of conformal gravity giving the same ISCO radius up to ω B ≤ 0.07 when N = 3 .

Testing gravity theories and their parameters using observations is an important issue in relativistic astrophysics. In this context, we investigate the motion of test particles and their harmonic oscillations in the spacetime of non-rotating hairy black holes (BHs) in Hordeski gravity, together with astrophysical applications of quasiperiodic oscillations (QPOs). We show possible values of upper and lower frequencies of twin-peak QPOs which may occur in the orbits from innermost stable circular orbits to infinity for various values of the Horndeski parameter q in relativistic precession, warped disk models, and three different sub-models of the epicyclic resonant model. We also study the behaviour of the QPO orbits and their position relative to innermost stable circular orbits (ISCOs) with respect to different values of the parameter q . It is obtained that at a critical value of the Horndeski parameter ISCO radius takes 6 M which has been in the pure Schwarzschild case. Finally, we obtain mass constraints of the central BH of microquasars GRS 1915+105 and XTE 1550-564 at the GR limit and the possible value of the Horndeski parameter in the frame of the above-mentioned QPO models. The analysis of orbits of twin peak QPOs with the ratio of upper and lower frequencies 3:2, around the BHs in the frame of relativistic precession (RP) and epicyclic resonance (ER4) QPO models have shown that the orbits locate close to the ISCO. It is obtained that the distance between QPO orbits and ISCO is less than the error of the observations.

Quasiperiodic oscillations (QPOs) are a powerful tool for testing gravity theories, probing gravitational and electromagnetic field properties, and obtaining constraints on the black hole and field parameters. This work considers charged particle dynamics near uniformly magnetized black holes in braneworlds. First, we obtain the solution of the Maxwell equation for magnetic fields and calculate the radial and angular magnetic field components. We derive and analyze the effective potential of charged particles for circular orbits and investigate the energy and angular momentum for the circular orbits. We also analyze the combined effects of magnetic interaction and braneworlds on the charged particles’ innermost stable circular orbits (ISCOs). We calculate the angular momentum of charged particles in Keplerian orbits in the presence of an external magnetic field and braneworlds. Also, we investigate frequencies of the particle oscillations along vertical and angular directions. We applied our studies on particle oscillations to the QPO studies in the relativistic precession model. Finally, we obtain constraints on magnetic interaction and braneworld parameters together with the black hole mass and QPO orbits using Monte Carlo Markov Chain (MCMC) simulation in the four-dimensional parameter space for the QPOs observed in the microquasars XTE J1550-564, GRO J1655-40 & GRS 1915-105, and at the center of galaxies M82 and Milky Way.

In this paper, we have presented the studies of the motion of magnetized particles and energetic processes around Schwarzschild black holes in modified gravity (MOG). The study of circular stable orbits shows that orbits of magnetized particles can not be stable for the values of magnetic coupling parameter β ≥ 1 . It was also shown that the range of stable circular orbits increases with the increase of both MOG and magnetic coupling parameters, while the effects of magnetic interaction stronger than the gravity. It was obtained that the increase of the MOG parameter causes the increase of center-of-mass energy collision of magnetized particles. Moreover, we have analyzed how to mimic the magnetic interaction with the spin of Kerr and Schwarzschild-MOG black holes. We have obtained that the magnetic coupling parameter can mimic the spin parameter a ≤ 0.15 ( a ≤ 0.28 ) giving the same radius of innermost contour(co)-rotating orbits at the values of the parameter β ∈ ( - 1 , 1 ) and the MOG parameter in the range α ∈ ( - 0.17 , 0.28 ) while the MOG parameter α ∈ ( - 0.7 , 0.9 ) mimics spin parameter of the black hole with the range | a | ∈ ( 0 , 1 ) .

In the present paper, we investigate the dynamics of magnetized particles around magnetically and electrically Reissner–Nordström (RN) black hole. The main idea of the work is to distinguish the effects of electric and magnetic charges of the RN black hole and spin of the rotating Kerr black hole through the dynamics of the magnetized particles. In this study, we have treated a magnetized neutron star as a magnetized test particle, in particular, the magnetar SGR (PSR) J1745-2900 orbiting around the supermassive black hole Sagittarius A* (SMBH SgrA*) with the magnetic interaction parameter b=0.716 and the parameter β=10.2. The comparison of the effects of the magnetic and electric charges, and magnetic interaction parameters on the dynamics of the magnetar modeled as a magnetized particle near the SMBH Sgr A* has shown that the magnetic charge of the RN black hole can mimic the spin parameter of a rotating Kerr black hole up to a/M≃0.82. The external magnetic field can mimic the magnetic charge of the RN black hole up to Qm/M=0.4465. We have shown that the electric charge of the RN black hole can mimic the black hole magnetic charge up to Qm/M=0.5482 and the magnetic field interaction with the magnetized particle acts against the increase of the mimicking value of the black hole spin parameter. The studies may be helpful to explain the observability of radio pulsars around the SMBH SgrA* system and taking it as a real astrophysical laboratory to get more precise constraints on the central black hole and dominated parameters of the alternate gravity. Finally, we have investigated the effects of magnetic and electric charge of the RN black hole in the center-of-mass energy of head-on collisions of magnetized particles with neutral, electrically charged, and magnetized particles. Both electric and magnetic charges of the RN black hole would lead to an increase in the center of the mass–energy of the collisions.