Circular Motion of Charged Particles near Charged Black Hole

We study the circular motion of charged particles near a charged black hole. The general form of the Lyapunov exponent of charged particles is obtained by using the Jacobian matrix. The results show that the chaos bound can be saturated by the circular motion of charged particles on the horizon. By further expanding the Lyapunov exponent near the horizon and investigating Reissner-Nordstr\"om(RN) black holes with different $M/Q$, we find that in contrast to the static equilibrium, the circular motion of charged particles can have a larger Lyapunov exponent due to the existence of angular momentum. For the RN black holes which have the mass-charge ratio $1<M/Q <1.1547$, the chaos bound is locally violated by the null and the time-like circular motion with large angular momentum. As an illustration of the universality of our results, we study the charged particles' circular motion near the Reissner-Nordstr\"om Anti-de Sitter (RN-AdS) black hole and find that the null and the time-like circular motion with large angular momentum can exceed the chaos bound under the background of RN-AdS black holes with the mass-charge ratio in the range $1.23132<M/Q<1.75225$.