https://doi.org/10.1140/epjc/s10052-024-12804-8
Regular Article - Theoretical Physics
Electromagnetic field and chaotic charged-particle motion around hairy black holes in Horndeski gravity
1
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, 201620, Shanghai, China
2
Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai, China
3
School of Mathematics and Statistics, Yunnan University, 650500, Kunming, China
Received:
9
December
2023
Accepted:
12
April
2024
Published online:
26
April
2024
The Wald vector potential is an exact solution of the source-less Maxwell equations regarding an electromagnetic field of a vacuum uncharged black hole like the Kerr background black hole in an asymptotically uniform magnetic field. However, it is not if the black hole is a nonvacuum solution in a theory of modified gravity with extra fields or a charged Kerr–Newman spacetime. To satisfy the source-less Maxwell equations in this case, the Wald vector potential must be modified and generalized appropriately. Following this idea, we derive an expression for the vector potential of an electromagnetic field surrounding a hairy black hole in the Horndeski modified gravity theory. Explicit symplectic integrators with excellent long-term behaviour are used to simulate the motion of charged particles around the hairy black hole immersed in the external magnetic field. The recurrence plot method based on the recurrence quantification analysis uses diagonal structures parallel to the main diagonal to show regular dynamics, but adopts no diagonal structures to indicate chaotic dynamics. The method is efficient to detect chaos from order in the curved spacetime, as the Poincaré map and the fast Lyapunov indicator are.
© The Author(s) 2024
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