Chaotic motion of particles around a dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe

TL;DR

This paper investigates chaotic geodesic motion around a dyonic Kerr-Newman black hole embedded in a Melvin-swirling universe, a six-parameter solution characterized by $M$, $Q$, $H$, $a$, $B$, and $j$. Using a corrected Runge-Kutta integration scheme and multiple chaos diagnostics—Poincaré sections, fast Lyapunov indicators, recurrence plots, bifurcation diagrams, and basins of attraction—the authors map how nonseparable dynamics arise from the interplay of the swirling parameter $j$ and magnetic field $B$. They find that increasing $j$ or $B$ expands chaotic regions and the number of chaotic orbits, while larger electric/magnetic charges and spin $a$ tend to suppress chaos, shifting the chaotic domains in parameter space. The results hold across sub-cases where conical singularities or Dirac strings are removed, indicating robust, richer chaotic dynamics in this spacetime with potential implications for particle dynamics near magnetized, rotating black holes.

Abstract

We employ the Poincaré section, fast Lyapunov indicator, recurrence analysis, bifurcation diagram and basins of attraction to investigate the dynamical behaviors of the motion of particles around a new dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe presented in [A. Di Pinto, S. Klemm, and A. Viganò, J. High Energy Phys. {\bf 06}, 150 (2025)]. We note that the swirling parameter $j$ and magnetic field strength $B$ make the equations of motion for particles nonseparable, and confirm the presence of chaotic behavior in the motion in this dyonic Kerr-Newman-Melvin-swirling spacetime and its sub-cases by removing the conical singularities and removing both the conical singularities and the Dirac strings. We observe that both the number of chaotic orbits and the chaotic region increase with the increase of the parameters $j$ and $B$, but decrease as the electric charge $Q$, magnetic charge $H$ or spin parameter $a$ increases. Moreover, we find that the presence of $j$ changes the ranges of $B$, $Q$, $H$ and $a$ where the chaotic motion appears for particles. The swirling parameter together with the magnetic field strength, electric charge, magnetic charge and spin parameter yields richer physics in the motion of particles for the spacetime of a dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe.

Figures (13)

• Figure 1: The change of the Poincaré section ($\theta = \frac{\pi}{2}$) with the swirling parameter $j$ for the motion of a particle around the dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe. Here we set $r(0) = 10.5$, $B = 10^{-4}$, $Q = 0.1$, $H = 0.1$, $a = 0.1$, $M = 1$, $E = 0.95$ and $L = 2.4M$.
• Figure 2: The change of the Poincaré section ($\theta = \frac{\pi}{2}$) with the swirling parameter $j$ for the motion of particles around the dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe. Here we set $B = 10^{-4}$, $Q = 0.1$, $H = 0.1$, $a = 0.1$, $M = 1$, $E = 0.95$ and $L = 2.4M$.
• Figure 3: The change of the Poincaré section ($\theta = \frac{\pi}{2}$) with the magnetic field strength parameter $B$ for the motion of particles around the dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe. Here we set $j = 10^{-6}$, $Q = 0.1$, $H = 0.1$, $a = 0.1$, $M = 1$, $E = 0.95$ and $L = 2.4M$.
• Figure 4: The change of the Poincaré section ($\theta = \frac{\pi}{2}$) with the electric charge parameter $Q$ (top, $H = 0.1$ and $a = 0.1$), magnetic charge parameter $H$ (middle, $Q = 0.1$ and $a = 0.1$) and spin parameter $a$ (bottom, $Q = 0.1$ and $H = 0.1$) for the motion of particles around the dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe. Here we set $j =10^{-5}$, $B =10^{-4}$, $M = 1$, $E = 0.95$ and $L = 2.4M$.
• Figure 5: The fast Lyapunov indicator (FLI) with the swirling parameter $j$ for the motion of particles shown in Fig. \ref{['fig1']}.