Violation of the chaos bound in charged Taub-NUT black holes

In this paper, we investigate the influence of the angular momentum of the charged particle around non-extremal and extremal charged Taub-NUT black holes on Lyapunov exponent, and find spatial regions where chaos bound is violated. The exponent is determined by the effective potential. When the particle's charge is fixed, circular orbits gradually move away from the event horizons with the angular momentum's increases. We find that the bound is always violated at a certain distance from the horizons when the angular momentum is greater than a certain value. Especially when the black holes' charges are small enough, the Lyapunov exponent's violation always exists for any value of the particle's angular momentum.