Chaos and dynamics of spinning particles in Kerr spacetime

TL;DR

This paper investigates the chaotic behavior of spinning particles around Kerr black holes using numerical methods and introduces a novel chaos detection indicator suitable for curved spacetime.

Contribution

It develops a new Fast Lyapunov Indicator for general relativity and explores the complex relationship between chaos, spin, and black hole parameters.

Findings

Chaos increases with particle spin magnitude S but not monotonically.

Kerr parameter a influences chaos occurrence inversely.

Particle spin affects orbital symmetry and can create equilibrium points.

Abstract

We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincar\'e sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial conditions, the orbits have equilibrium points.