Mathematical analysis of chaotic particle motion near a charged Kalb-Ramond black hole: Impact of angular momentum and Lorentz symmetry breaking

In this work, we investigate the trajectories of a charged test particle in the spacetime of a charged Kalb–Ramond black hole under a small violation of Lorentz symmetry. Our aim is to determine the conditions under which the particle’s motion transitions to chaotic behavior. The study focuses on the influence of three key parameters: the black hole’s charge, the Lorentz symmetry-breaking term, and the particle’s angular momentum. The results show that increasing the black hole charge initially reduces both the event horizon radius and the effective gravitational pull; however, at larger charge values, curvature effects lead to a reversal, causing both quantities to increase again. The Lorentz-breaking parameter shows a comparable influence on the horizon properties. In contrast, larger angular momentum generally stabilizes the orbit and suppresses chaotic motion. Poincaré sections are used to visualize the transition between regular and chaotic behavior. Overall, the results show that Lorentz symmetry breaking affects the near-horizon structure and the stability of particle motion, with possible implications for black hole shadows, accretion disk variability, and quasi-periodic oscillations. We would like to mention that the present work differs from our earlier analysis of string dynamics, as we study the chaotic motion of a charged test particle using phase-space and Lyapunov techniques.