Dynamics of Charged Particles Moving around Kerr Black Hole with Inductive Charge and External Magnetic Field

Wu, Xiaoxia; Wang, Yu; Deng, Chen; Liu, Baorong; Liang, En‐Wei

doi:10.3390/universe7110410

Cited by 15 publications

(18 citation statements)

References 73 publications

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“…Such symmetric products are a component of symplectic operators of second order. The symplectic method S 2 is an extension to the works of [83][84][85] regarding the time-transformed explicit symplectic methods for the Kerr spacetimes. Of course, such symmetric products of order 2 easily yield a fourth-order construction of Yoshida [87]:…”

Section: Design Of Algorithmsmentioning

confidence: 99%

“…Recently, the authors of [80][81][82] successfully constructed the explicit symplectic integrators for the Schwarzschild-type black holes with or without external magnetic fields by splitting the corresponding Hamiltonians into several parts having analytical solutions as explicit functions of proper time. More recently, the time-transformed explicit symplectic integrators were designed for the Kerr family spacetimes [83][84][85].…”

Section: Introductionmentioning

confidence: 99%

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Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity

et al. 2021

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A small deformation to the Schwarzschild metric controlled by four free parameters could be referred to as a nonspinning black hole solution in alternative theories of gravity. Since such a non-Schwarzschild metric can be changed into a Kerr-like black hole metric via a complex coordinate transformation, the recently proposed time-transformed, explicit symplectic integrators for the Kerr-type spacetimes are suitable for a Hamiltonian system describing the motion of charged particles around the non-Schwarzschild black hole surrounded with an external magnetic field. The obtained explicit symplectic methods are based on a time-transformed Hamiltonian split into seven parts, whose analytical solutions are explicit functions of new coordinate time. Numerical tests show that such explicit symplectic integrators for intermediate time steps perform well long-term when stabilizing Hamiltonian errors, regardless of regular or chaotic orbits. One of the explicit symplectic integrators with the techniques of Poincaré sections and fast Lyapunov indicators is applied to investigate the effects of the parameters, including the four free deformation parameters, on the orbital dynamical behavior. From the global phase-space structure, chaotic properties are typically strengthened under some circumstances, as the magnitude of the magnetic parameter or any one of the negative deformation parameters increases. However, they are weakened when the angular momentum or any one of the positive deformation parameters increases.

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Section: Design Of Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity

et al. 2021

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“…However, they are integrable because enough conserved quantities of motion are present. When these black holes suffer from some perturbations, such as external magnetic field [57][58][59][60] and the discs or rings around black holes [61,62], the spacetimes may be non-integrable. In this case, chaos may occur.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a class of explicit symplectic integrators was designed for black-hole spacetimes in general relativity [57,58,[67][68][69]74,99]. By dividing the Hamiltonians or timetransformed Hamiltonian corresponding to the spacetimes into multiple parts, the authors used the analytical solutions of the splitting parts to compose a set of explicit symplectic integrators.…”

Section: Introductionmentioning

confidence: 99%

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Chaos in a Magnetized Brane-World Spacetime Using Explicit Symplectic Integrators

Huang

2022

Universe

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A brane-world metric with an external magnetic field is a modified theory of gravity. It is suitable for the description of compact sources on the brane such as stars and black holes. We design a class of explicit symplectic integrators for this spacetime and use one of the integrators to investigate how variations of the parameters affect the motion of test particles. When the magnetic field does not vanish, the integrability of the system is destroyed. Thus, the onset of chaos can be allowed under some circumstances. Chaos easily occurs when the electromagnetic parameter becomes large enough. Dark matter acts as a gravitational force, so that chaotic motion can become more obvious as dark matter increases. The gravity of the black hole is weakened with an increasing positive cosmological parameter; therefore, the extent of chaos can be also strengthened. The proposed symplectic integrator is applied to a ray-tracing method and the study of such chaotic dynamics will be a possible reference for future studies of brane-world black hole shadows with chaotic patterns of self-similar fractal structures based on the Event Horizon Telescope data for M87* and Sagittarius A*.

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Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems

Zhu¹,

Ji²,

Zhu³

et al. 2023

Chinese Phys. B

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We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge-Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge-Kutta and Runge-Kutta-Nyström explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge-Kutta and Runge-Kutta-Nyström extended phase space symplectic-like methods with the midpoint permutation.

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Dynamics of Charged Particles Moving around Kerr Black Hole with Inductive Charge and External Magnetic Field

Cited by 15 publications

References 73 publications

Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity

Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity

Chaos in a Magnetized Brane-World Spacetime Using Explicit Symplectic Integrators

Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems

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