Presence of horizon makes particle motion chaotic

TL;DR

This paper investigates how the presence of a black hole horizon induces chaos in the motion of a massless, chargeless particle, with chaos characterized by exponential growth and Lyapunov exponents bounded by surface gravity.

Contribution

It demonstrates that horizons can induce chaos in particle motion near black holes, extending understanding to both static and rotating black hole spacetimes.

Findings

Radial motion near horizons exhibits exponential growth.

Lyapunov exponent is bounded by the surface gravity.

Rotation enhances chaotic behavior.

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.