We study the static equilibrium of a charged massive particle around a charged black hole, balanced by the Lorentz force. For a given black hole, the equilibrium surface is determined by the charge/mass ratio of the particle. By investigating a large class of charged black holes, we find that the equilibria can be stable, marginal or unstable. We focus on the unstable equilibria which signal chaotic motions and we obtain the corresponding Lyapunov exponents $λ$. We find that although $λ$ approaches universally the horizon surface gravity $κ$ when the equilibria are close to the horizon, the proposed chaotic motion bound $λ<κ$ is satisfied only by some specific black holes including the RN and RN-AdS black holes. The bound can be violated by a large number of black holes including the RN-dS black holes or black holes in Einstein-Maxwell-Dilaton, Einstein-Born-Infeld and Einstein-Gauss-Bonnet-Maxwell gravities. We find that unstable equilibria can even exist in extremal black holes, implying that the ratio $λ/κ$ can be arbitrarily large for sufficiently small $κ$. Our investigation does suggest a universal bound for sufficiently large $κ$, namely $λ/κ<{\cal C}$ for some order-one constant ${\cal C}$.
Horizon--orbit scale competition underlying chaos bound violation for spinning particles
School of Science, Xihua University（西华大学理学院）；Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力实验室引力波实验中心）
Chaos bound violation by spinning particles in Gauss-Bonnet-AdS black holes
School of Mathematics, Physics and Statistics, Sichuan Minzu College（四川民族学院数理统计学院）；School of Physics and Astronomy, China West Normal University（西华师范大学物理与天文学院）
