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Near-horizon behavior of nonequatorial accelerated particle motion and high energy particle collisions

H. V. Ovcharenko

O. B. Zaslavskii

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Phys. Rev. D 112, 084002 – Published 2 October, 2025

DOI: https://doi.org/10.1103/kjk7-pyvj

Abstract

We consider the motion of a particle in the background of a stationary axially symmetric generic black hole. A particle experiences the action of a force of unspecified nature. We require the force to remain finite in a comoving frame. The result is expressed in terms of several integers characterizing the Taylor expansion of the metric coefficients near the horizon. We show that the polar component of the four-velocity remains finite. As a result, the scenarios of high energy particle collisions, found previously in the context of the BSW effect for equatorial motion, do not change qualitatively in the nonequatorial case. The fact that the polar component is finite, also enables us to fill some gaps in the description of the BSW effect in previous works. This includes (i) classification of particle trajectories for nonequatorial motion, (ii) more coherent derivation of kinematics of the BSW effect, and (iii) discussion of bands in which the BSW effect takes place. Our results have a quite general character and can be used not only in description of high energy particle collisions but also in diverse astrophysical problems for which motion is not constrained by the equatorial plane.

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References (21)

  1. M. Bañados, J. Silk Pand, and S. M. West, Kerr black holes as particle accelerators to arbitrarily high energy, Phys. Rev. Lett. 103, 111102 (2009).
  2. A. A. Grib and Yu. V. Pavlov, On particles collisions in the vicinity of rotating black holes, Pis’ma Zh. Eksp. Teor. Fiz. 92, 147 (2010) [JETP Lett. 92, 125 (2010)].
  3. O. B. Zaslavskii, Acceleration of particles as universal property of rotating black holes, Phys. Rev. D 82, 083004 (2010).
  4. T. Harada and M. Kimura, Collision of two general geodesic particles around a Kerr black hole, Phys. Rev. D 83, 084041 (2011).
  5. O. B. Zaslavskii, Ultra-high energy collisions of nonequatorial geodesic particles near dirty black holes, J. High Energy Phys. 12 (2012) 032.
  6. H. V. Ovcharenko and O. B. Zaslavskii, Bañados-Silk-West effect with finite forces near different types of horizons: General classification of scenarios, Phys. Rev. D 108, 064029 (2023).
  7. H. V. Ovcharenko and O. B. Zaslavskii, Bañados-Silk-West phenomenon for near-fine-tuned particles with an external force: General classification of scenarios, Phys. Rev. D 109, 124041 (2024).
  8. D. E. A. Gates and S. Hadar, Signatures of particle collisions near extreme black holes, Phys. Rev. D 109, 024052 (2024).
  9. J. M. Bardeen, W. H. Press, and S. A. Teukolsky, Rotating black holes: Locally nonrotating frames, energy extraction, and scalar synchrotron radiation, Astrophys. J. 178, 347 (1972).
  10. Black Holes: The Membrane Paradigm, edited by K. S. Thorne, R. H. Price, and D. A. Macdonald (Yale University Press, London, 1986).
  11. O. B. Zaslavskii, Acceleration of particles by black holes: Kinematic explanation, Phys. Rev. D 84, 024007 (2011).
  12. T. Piran and J. Shaham, Upper bounds on collisional Penrose processes near rotating black hole horizons, Phys. Rev. D 16, 1615 (1977).
  13. H. V. Ovcharenko and O. B. Zaslavskii, Axially symmetric rotating black holes, Boyer–Lindquist coordinates, and regularity conditions on horizons, Gravit. Cosmol. 29, 269 (2023).
  14. H. Maeda and C. Martinez, Existence and absence of Killing horizons in static solutions with symmetries, Classical Quantum Gravity 41, 245013 (2024).
  15. K. A. Bronnikov, E. Elizalde, S. D. Odintsov, and O B Zaslavskii, Horizons vs. singularities in spherically-symmetric space-times, Phys. Rev. D 78, 064049 (2008).
  16. O. B. Zaslavskii, Acceleration of particles by black holes—A general explanation. Classical Quantum Gravity 28, 105010 (2011).
  17. O. B. Zaslavskii, High energy particle collisions near the bifurcation surface, Int. J. Mod. Phys. D 22, 1350044 (2013).
  18. H. V. Ovcharenko and O. B. Zaslavskii, Naked and truly naked rotating black holes, J. Math. Phys. (N.Y.) 66, 042502 (2025).
  19. A. V. Toporensky and O. B. Zaslavskii, Flow and peculiar velocities for generic motion in spherically symmetric black holes, Gravitation Cosmol. 27, 126 (2021).
  20. P. Gusin, B. Kusnierz, and A. Radosz, Observers in spacetimes with spherical and axial symmetries, arXiv:1507.01617.
  21. I. V. Tanatarov and O. B. Zaslavskii, Collisional super-Penrose process and Wald inequalities, Gen. Relativ. Gravit. 49, 119 (2017).

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Phys. Rev. D 112, 084002– Published 2 October, 2025
  • Received 16 May 2025
  • Accepted 12 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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