Chaotic behaviors of particles around the black hole with an anisotropic matter immersed in a magnetic field

Khusan Alibekov; Hocheol Lee; Pakhlavon Yovkochev; Bobomurat Ahmedov; Bum-Hoon Lee; Ahmadjon Abdujabbarov; Wonwoo Lee

doi:10.1103/195k-3k3m

Chaotic behaviors of particles around the black hole with an anisotropic matter immersed in a magnetic field

Khusan Alibekov^1,*, Hocheol Lee ^2,†, Pakhlavon Yovkochev ^3,10,‡, Bobomurat Ahmedov ^4,5,8,§, Bum-Hoon Lee^6,7,9,∥, Ahmadjon Abdujabbarov^4,5,8,¶, and Wonwoo Lee ^6,**

¹Department of Physics and Astronomy, Faculty of Physical Sciences and Engineering, University of Southampton, Southampton SO17 1BJ, United Kingdom
²Department of Physics, Dongguk University, Seoul 04620, Korea
³Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent 100000, Uzbekistan
⁴Ulugh Beg Astronomical Institute of the Uzbekistan Academy of Sciences, Astronomy Street 33, Tashkent 100052, Uzbekistan
⁵Institute of Theoretical Physics, National University of Uzbekistan, Tashkent 100174, Uzbekistan
⁶Center for Quantum Spacetime, Sogang University, Seoul 04107, Korea
⁷Department of Physics, Sogang University, Seoul 04107, Korea
⁸School of Physics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
⁹Department of Physics, Shanghai University, 99 Shangda Road, Shanghai 200444, China
¹⁰Samarqand State Pedagogical Institute, Spitamen Shokh Street 166, Samarkand 140100, Uzbekistan

^*Contact author: K.A.U.Alibekov@soton.ac.uk
^†Contact author: insaying@dongguk.edu
^‡Contact author: yovqochevp@gmail.com
^§Contact author: ahmedov@astrin.uz
^∥Contact author: bhl@sogang.ac.kr
^¶Contact author: ahmadjon@astrin.uz
^**Contact author: warrior@sogang.ac.kr

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Phys. Rev. D 114, 084056 – Published 20 October, 2026

DOI: https://doi.org/10.1103/195k-3k3m

Abstract

We present an exact solution to the Einstein-Maxwell equations that describes a static black hole coexisting with anisotropic matter immersed in an external magnetic field, obtained via the Harrison transformation. Our findings reveal that an increase in the anisotropic matter parameter systematically suppresses the local chaotic behavior, as indicated by a reduction in the Lyapunov exponent. Conversely, variations in the external magnetic field lead to qualitative changes in global chaotic behavior. This is analyzed through Poincaré sections, which demonstrate transitions between regular and chaotic trajectories resulting from the nonlinear gravitational-magnetic interactions. These factors play distinct yet complementary roles in shaping chaotic particle dynamics around black holes. This study would offer a new theoretical framework for exploring nonintegrable particle motion within magnetized black hole spacetimes.

Physical Review D

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Chaotic behaviors of particles around the black hole with an anisotropic matter immersed in a magnetic field

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