In this paper, we aim to investigate the dynamics of magnetized particles around magnetically and electrically charged static black holes (BHs) in Einstein–Maxwell-scalar theory. First, we explore the possible values of EMS parameters for which the spacetime geometry represents a BH spacetime. Since there is no interaction between the electric field of the electrically charged BH and the proper magnetic field of the magnetized test particle. Therefore, we consider BH immersed in an external asymptotically uniform magnetic field. We explore the properties of an external magnetic field around a charged EMS BH. Moreover, we also explored the effects of BH charge and EMS theory parameters on particle’s energy and angular momentum in the circular stable orbits, together with the radius of innermost stable circular orbits. All the obtained results are compared with the acquired results of the Reissner–Nordström BH. Finally, we investigate the behaviour of the center of mass energy of colliding magnetized and electrically charged particles around the EMS BH.

General relativity (GR) is a well-tested theory of gravity in strong and weak field regimes. Many modifications to this theory were obtained, including different scalar, vector, and tensor fields to the GR with non-minimal coupling to gravity. Kalb–Ramond (KR) gravity is also a modified theory formulated in the presence of a bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BH). In this work, we study the circular motion of charged particles and explore energetic processes around charged BHs in KR theory. First, we investigated the event horizon radius and analyzed horizon-no horizon regions in the BH charge and KR parameter space. Considering the Coulomb interaction, we derive and analyze the effective potential for charged particles around a charged KR BH. We investigate charged particles’ angular momentum and energy corresponding to circular orbits. We also investigate how the KR non-minimal coupling parameter affects the radius of the innermost stable circular orbits, the corresponding energy, and the angular momentum. We also investigated the electric Penrose process and charged-particle collisions near the KR BH. The presence of the nonzero KR parameter results in a decrease in the energy efficiency of the Penrose process. Also obtained is that the KR parameter’s positive (negative) values cause a decrease (increase) in the center of mass energy of colliding particles near the BH horizon.

No-hair theorem indicates that black holes cannot have their own magnetic dipole moment. They can be weakly magnetized in binary systems with a neutron star companion and an accretion disc of charged particles. A simple model suggested by Petterson states that a current loop accreting a Schwarzschild black hole generates dipole-like magnetic fields in the outer region of the loop that are uniform in the inner region. This study considers circular motion and collisions of charged test particles with magnetic dipole moments in the inner and outer regions. First, we derive the effective potential taking into account the magnetic interactions between external magnetic fields with electric charge and the magnetic dipole moment of the particle. We investigate the possible innermost stable circular orbits (ISCOs) of the charged and magnetized particles orbiting the magnetized Schwarzschild black hole inside and outside the current loop. Finally, we explore the collisional processes of these particles near the black hole horizons, examining the effects of magnetic interactions on the critical angular momentum of particles that may collide and the center of mass energy of the colliding particles. We discuss astrophysical relevant objects with magnetic dipole moment and electric charge: magnetized neutron stars, white dwarfs, rotating stellar-mass black holes, electrons, and protons, and also estimate the interaction parameters for them.

We investigate the dynamics of test particles endowed with both electric charge and a magnetic dipole moment around a Schwarzschild black hole (BH) immersed in an externally asymptotically uniform magnetic field. We further analyse the effective potential and specific angular momentum and energy of the particles. Furthermore, we show that the upper limit for magnetic interaction parameter $\beta$ increases with increasing cyclotron frequency ${\omega }_{\mathrm{B}}$, while the radius of the innermost stable circular orbit (ISCO) for charged test particles decreases for the upper value of $\beta ={\beta }_{\mathrm{upper}}$. Furthermore, we show that the energy efficiency released from the BH increases up to about 90% due to the presence of the magnetic dipole moment of the test particle. We explore a degeneracy between the spin parameter of rotating Kerr BH and the magnetic parameter for the values of the ISCO radius and energy efficiency. We study in detail the centre of mass energy for collisions of charged and magnetized particles in the environment surrounding the Schwarzchild BH. Finally, as an astrophysical application, we explore the magnetized parameter and cyclotron frequency numerically for a rotating magnetized neutron star. Interestingly, we show that the corresponding values of the above-mentioned parameters for the magnetar PSR J1745-2900 that orbits around the supermassive black hole (SMBH) that exists at the centre of the Milky Way galaxy are ${\omega }_{\mathrm{B}}\simeq 5$ and $\beta \simeq 0.67$, respectively, for the magnetic field is about 10 G.

In this study, we investigate the influence of the parameters of ModMax nonlinear electrodynamics and perfect-fluid dark matter (PFDM) on the geometry and physical properties of charged black holes. A static, spherically symmetric solution to the Einstein field equations describing a charged ModMax black hole immersed in a PFDM background is obtained. The motion of charged test particles in this spacetime is analyzed in detail, including the effective potential, the conditions for stable and unstable circular orbits, and the radius of the innermost stable circular orbit (ISCO). It is shown that the ModMax parameter γ shifts the orbits outward for repulsive Coulomb interactions and inward for attractive forces, while increasing PFDM enhances gravitational attraction, shifting the ISCO inward. Furthermore, the interactions and collisions of charged particles near the event horizon are examined. The center-of-mass energy exhibits the characteristic behavior in charged-particle collisions, rapidly increasing as the particles approach the horizon. The parameter γ amplifies the BSW acceleration mechanism, while α suppresses it. The electric Penrose process for charged particles is also examined, revealing that the efficiency of energy extraction increases with the black hole charge and is strongly influenced by the interaction parameter γ , which plays a dominant role in enhancing the efficiency, whereas the effect of α remains comparatively negligible.