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Spinning charged test particle dynamics around a Schwarzschild black hole embedded in a homogeneous magnetic field

Misbah Shahzadi1,*, Martin Kološ2,†, Ondřej Zelenka1,‡, and Georgios Lukes-Gerakopoulos1,3,§

  • *Contact author: misbahshahzadi51@gmail.com
  • †Contact author: martin.kolos@physics.slu.cz
  • ‡Contact author: ondrej.zelenka@asu.cas.cz
  • §Contact author: gglukes@gmail.com
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Phys. Rev. D 114, 024085 – Published 29 July, 2026

DOI: https://doi.org/10.1103/jp9y-5qwl

Abstract

We study the dynamics of spinning charged test particles orbiting a Schwarzschild black hole immersed in a test uniform magnetic field. This setup provides a simple but physically relevant framework for modeling particle motion in magnetized astrophysical environments near compact objects, where both spin-curvature coupling and electromagnetic interactions can play a significant role. The particle trajectories are obtained numerically in both equatorial and off-equatorial configurations, allowing us to examine the influence of spin-curvature and Lorentz forces on the motion. In the equatorial plane, assuming the particle’s spin vector is orthogonal to the orbital plane, we derive analytical expressions for the conserved energy and angular momentum, as well as for the radial and orbital frequencies as functions of spin parameter and magnetic parameter. We also construct the corresponding effective potential to determine the allowed regions of particle motion. The equatorial dynamics remain integrable due to the existence of conserved quantities associated with the spacetime symmetries and the alignment of the magnetic field. In contrast, the off-equatorial motion constitutes a nonintegrable dynamical system. While limiting subcases of the system, i.e., the spinning neutral and nonspinning charged cases, can be analyzed using two-dimensional Poincaré surface of sections, the combined system can be reduced only up to three degrees of freedom. Hence, to investigate the resulting complexity, we analyze the phase space using four-dimensional Poincaré surface of sections along with recurrence analysis, revealing the presence of chaotic behavior for particular choices of parameters and initial conditions. Finally, we compare the dynamics of spinning charged test particles with the limiting cases of nonspinning neutral, spinning neutral, and nonspinning charged particles, thereby distinguishing the respective contributions of spin-curvature and electromagnetic interactions.

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Phys. Rev. D 114, 024085– Published 29 July, 2026
  • Received 6 May 2026
  • Accepted 30 June 2026
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