Chaos of Particle Motion near the Black Hole with Quasi-topological Electromagnetism

We explore the chaotic behavior of particle motion in a black hole with quasi-topological electromagnetism. The chaos bound is found to be violated in the higher order expansion of the metric function and the electric potential near the horizon. We draw the Poincare sections of particle motion corresponding to the chaos bound violated and non-violated cases, respectively. Then we study the relationship between the maximal Lyapunov exponent \lambda_s defined by the static equilibrium and the Lyapunov exponent of the particle geodesic motion near the Reissner-Nordstrom(RN) black hole and the black hole with quasi-topological electromagnetism. We find an interesting relationship between the Lyapunov exponent \lambda_{ph} of photon's radial falling into the black hole and the maximal Lyapunov exponent \lambda_s. For the black holes whose metric function increases monotonically with radius outside horizon, this leads to \lambda_{ph} \geq 2\lambda_s.