Presence of horizon makes particle motion chaotic

Abstract

We analyze the motion of a {\it massless} and {\it chargeless} particle very near to the event horizon. It reveals that the radial motion has exponential growing nature which indicates that there is a possibility of inducing chaos in the particle motion of an integrable system when it comes under the influence of the horizon. This is being confirmed by investigating the Poincar$\acute{e}$ section of the trajectories with the introduction of a harmonic trap to confine the particle's motion. Two situations are investigated: (a) {\it any} static, spherically symmetric black hole and, (b) spacetime represents a stationary, axisymmetric black hole (e.g., Kerr metric). In both cases, the largest Lyapunov exponent has upper bound which is the surface gravity of the horizon. We find that the inclusion of rotation in the spacetime introduces more chaotic fluctuations in the system. The possible implications are finally discussed.