Chaotic orbits for spinning particles in Schwarzschild spacetime

TL;DR

This paper investigates chaotic orbits of spinning particles in Schwarzschild spacetime, revealing chaos at smaller, astrophysically relevant spin values using Lyapunov exponents and Poincaré maps.

Contribution

It introduces a new method for comparing Lyapunov exponents and demonstrates chaos occurs at lower spins than previously known.

Findings

Chaotic orbits exist at smaller spin values than previously identified.

Developed a novel method for comparing Lyapunov exponents.

Chaotic orbits could be astrophysically relevant.

Abstract

We consider the orbits of particles with spin in the Schwarzschild spacetime. Using the Papapetrou-Dixon equations of motion for spinning particles, we solve for the orbits and focus on those that exhibit chaos using both Poincar\'e maps and Lyapunov exponents. In particular, we develop a method for comparing the Lyapunov exponents of chaotic orbits. We find chaotic orbits for smaller spin values than previously thought and with spins that could be realized astrophysically.