We study the dynamics of (i) neutral test particles, (ii) magnetically charged test particles, and (iii) test magnetic dipole around a regular Bardeen black hole surrounded by perfect fluid dark matter (PFDM). It has been shown how the magnetic charge of the black hole and the parameter of the surrounding PFDM can influence the innermost stable circular orbit (ISCO) radius of a test particle. We have found that the ISCO radius is strongly affected as a consequence of the combined effect of the magnetic charge parameter and the perfect fluid dark matter. The black hole magnetic charge parameter $g$ and the combined effect of perfect fluid dark matter can mimic the black hole rotation parameter up to $a/M\approx 0.9$. It has been observed that the ISCO for magnetic dipole disappears at the values exceeding the calculated upper value for the magnetic interaction parameter $\beta$. The upper limit decreases with the increase of both the dark matter and magnetic charge parameters. Finally, as an astrophysical application, we have analyzed degeneracy effects of spin of Kerr black holes and magnetic charge of regular Bardeen black holes for the different values of the dark matter parameter providing exactly the same value for ISCO radius of a magnetic dipole with the same value of the parameter $\beta =10.2$ of the magnetar called PSR J1745-2900 orbiting around supermassive black hole Sagittarius A*. It has been observed that the magnetic charge of the pure regular Bardeen black hole can mimic the spin of a Kerr black hole up to $a/M\simeq 0.8085$, while upper limit for the magnetic charge which may provide ISCO for the magnetic dipole is $g_{\text{upper}}\simeq 0.65M$. In the presence of PFDM with the parameter $\alpha =0.01(0.05)$, the upper limit for the magnetic charge decreases and equals to $g_{\text{upper}}\simeq 0.62M$ ($0.548M$) and consequently mimicker value for the spin parameter of black hole lies in the range of $a/M\in (0.0106÷0.8231)$ ($a/M\in (0.0816÷0.8595)$). We also show that the same values of the spin of Kerr black hole and the magnetic charge of regular Bardeen black hole surrounded by PFDM provide the same values for the ISCO radius of the chosen magnetar.

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.

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.

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*.