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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 $$\beta \ge 1$$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 $$a \le 0.15$$a≤0.15 ($$a \le 0.28$$a≤0.28) giving the same radius of innermost contour(co)-rotating orbits at the values of the parameter $$\beta \in (-1,1)$$β∈(-1,1) and the MOG parameter in the range $$\alpha \in (-0.17,0.28)$$α∈(-0.17,0.28) while the MOG parameter $$\alpha \in (-0.7, 0.9)$$α∈(-0.7,0.9) mimics spin parameter of the black hole with the range $$|a| \in (0,1)$$|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 $$b=0.716$$ b = 0.716 and the parameter $$\beta =10.2$$ 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 $$a/M \simeq 0.82$$ a / M ≃ 0.82 . The external magnetic field can mimic the magnetic charge of the RN black hole up to $$Q_m/M=0.4465$$ Q m / M = 0.4465 . We have shown that the electric charge of the RN black hole can mimic the black hole magnetic charge up to $$Q_m/M=0.5482$$ Q m / 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.

Neutron stars (NS)s are astrophysical objects with strong gravitational and electromagnetic fields. Since there are several effects on radiation processes around the star, it is impossible to consider whole effects all together. One way to study the processes is by considering them one by one as a toy model. In this paper, we have investigated the effects of spacetime deformation on the surface magnetic field of the slowly rotating neutron star and its plasma magnetospheric processes, such as the plasma magnetosphere formation around the star. At first, the approximate vacuum solutions of the Maxwell equations for the electromagnetic fields of a magnetized neutron star in a slowly rotating deformed spacetime metric have been obtained. It has been shown that the positive deformation parameter leads to an increase in the value of the (surface) magnetic field at the near zone of the neutron star, while the effect of the negative deformation parameter is vice versa. We have also considered the electric field of the slowly rotating neutron star in the spacetime. In the slow rotation approximation, we have studied the particle acceleration in the polar cap zone, considering the effect of deformation of spacetime on the [Formula: see text]-Lorentz factor of a relativistic charged particle. It is shown that in the case of the positive deformation, an additional gravity occurs around the NS. The effects of spacetime deformation on magneto-dipolar radiation of radio pulsars and polar cap size have also been studied and shown that negative deformation of spacetime increased the radiation luminosity and as positive deformation increases, the luminosity decreases. Size of polar cap region of a neutron star, where magnetic field lines open, increases with increasing the value of the deformation parameter [Formula: see text]. Moreover, we have studied the influence of the spacetime deformation on the death line for radio pulsar, which separates the region in [Formula: see text] [Formula: see text] diagram, where the pulsar can or cannot radiate in radio band (create pair production) through inverse compton scattering (ICS). It is shown that the negative (positive) deformation shifts upward (downward) the death line, which means that even a small negative (positive) deformation of spacetime may cause to be radio-quite (be radio load) the radio pulsar which is lying on the death line (in [Formula: see text] diagram) in the GR frame with its corresponding parameters.

The analytical expression for Goldreich-Julian (GJ) charge density at the polar cap of magnetized neutron star has been obtained in braneworlds for inclined neutron star through solving Maxwell equations and shown that the value of GJ charge density decreases with increasing the value of the brane charge. The analytical expressions for scalar potential and parallel electric field on the region greater than the polar cap region of the neutron star have also been obtained by solving Poisson equation in braneworlds.