Chaotic dynamics of string around a charged Kalb–Ramond black hole with Lorentz symmetry breaking

The dynamics of a relativistic string close to a charged Kalb-Ramond black hole’s boundary is examined in this article. We show that the development of the string is extremely chaotic and often surpasses the Maldacena–Shenker–Stanford constraint, using the Lyapunov exponent as a diagnostic instrument. Our study also shows that the string’s energy and rotational momentum are crucial in determining its dynamic properties. By increasing the Lorentz symmetry-breaking parameter, the event horizon radius decreases, while the surface gravity increases. Furthermore, when all other parameters are fixed and the angular momentum $L$ is varied, it is observed that for inner points, increasing $L$ leads to a decrease in the values of ${\lambda }^2-{\kappa }^2$ , whereas for outer points, increasing $L$ results in an increase in ${\lambda }^2-{\kappa }^2$ . Similarly, when $L$ and other parameters are kept constant and the energy $E$ is varied, the behavior differs: for inner points, increasing $E$ causes ${\lambda }^2-{\kappa }^2$ to rise, indicating stronger chaotic behavior; in contrast, for outer points, increasing $E$ leads to a decrease in ${\lambda }^2-{\kappa }^2$ , suggesting a tendency toward satisfying the Maldacena–Shenker–Stanford bound. Furthermore, we find that a higher energy in the case of outer points suppresses chaotic behavior, as evidenced by a decreasing Lyapunov exponent. These findings contribute to a deeper understanding of chaotic geodesics and the role of Lorentz-symmetry violation in modified gravity frameworks.