Chaotic orbits for spinning particles in Schwarzschild spacetime

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.