Eur. Phys. J. Plus (2026) 141: 500
https://doi.org/10.1140/epjp/s13360-026-07707-4

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Magnetic fields and magnetized particles around black holes in braneworlds

¹ Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, 100000, Tashkent, Uzbekistan
² University of Tashkent for Applied Sciences, Str. Gavhar 1, 100149, Tashkent, Uzbekistan
³ Tashkent State Technical University, 100095, Tashkent, Uzbekistan
⁴ Institute of Theoretical Physics, National University of Uzbekistan, University Str. 4, 100174, Tashkent, Uzbekistan
⁵ Kimyo International University in Tashkent, Shota Rustaveli street 156, 100121, Tashkent, Uzbekistan
⁶ New Uzbekistan University, Movarounnahr Str. 1, 100000, Tashkent, Uzbekistan
⁷ Urgench State University, Kh. Alimdjan str. 14, 100121, Urgench, Uzbekistan
⁸ Department of Solid State Physics, Samarkand State University, University Avenue 15, 140104, Samarkand, Uzbekistan
⁹ University of World Economy and Diplomacy, Mustakillik Ave. 54, 100007, Tashkent, Uzbekistan

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Received: 9 January 2026
Accepted: 16 April 2026
Published online: 5 May 2026

Abstract

This paper studies the motion and interactions of particles with magnetic dipole moments in the vicinity of magnetized black holes in the braneworld model. The analysis begins by solving Maxwell’s equations for the electromagnetic potentials in the presence of an external uniform magnetic field, incorporating the brane parameter’s influence on the field’s radial and angular components. The effective potential governing particle dynamics is derived, and expressions for the energy and angular momentum of circular orbits are obtained. Particular attention is given to the role of the tidal charge and magnetic interaction parameter in determining the location and stability of circular orbits. The innermost stable circular orbit (ISCO) is examined in detail, showing that an increase in the brane parameter shifts the ISCO inward, while a stronger magnetic interaction pushes it outward. The study also explores collisions of magnetized particles near the black hole horizon. Conditions for critical angular momentum are identified, highlighting the thresholds that separate bound orbits from plunging or escaping trajectories. The center-of-mass energy of the colliding particles is then computed, revealing how both brane effects and magnetic interactions affect it. The results demonstrate that while braneworld corrections enhance collision energies, strong magnetic coupling suppresses them, thereby moderating the unbounded values predicted in simpler models. These findings offer new insights into the dynamics of magnetized matter near black holes, providing potential observational signatures relevant to high-energy astrophysical processes, such as accretion flows, cosmic-ray acceleration, and the formation of relativistic jets.