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Particles with electric charge and magnetic dipole moment around Einstein-Æther black holes in magnetic fields: Circular orbits and collisions
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DOI：10.1016/j.aop.2026.170609.png)
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Abstract
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We study the motion of charged and magnetized test particles in the spacetime of a static, spherically symmetric Einstein-æther black hole immersed in an external asymptotically uniform magnetic field. Solving Maxwell’s equations, we obtain an exact vector-potential solution that makes the dependence of the magnetic-field structure on the coupling parameters explicit. The resulting geometry shows notable deviations from the Schwarzschild case near the black hole horizons. Using the effective-potential formalism, we analyze how the magnetic field–dipole interaction and the field affect the stability of circular orbits, the innermost stable circular orbits (ISCOs), and the energy and angular momentum at the ISCO. We find that magnetic coupling generally shifts the ISCO inward, whereas æther couplings shift it outward, partially mitigating its effects. We further calculate the center-of-mass energy of head-on collisions of magnetized particles and analyze the effects of æther and magnetic fields on the energy in various scenarios. These findings suggest that precise observations of inner-disk edges as described by ISCOs, high-energy spectra of the accretion disc, and the behavior of relativistic magnetized plasma around black holes may also help us understand æther gravity.
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