Spinning particles moving around black holes: integrability and chaos

TL;DR

This paper investigates the dynamics of spinning particles around black holes, analyzing their integrability and chaos, with a focus on Schwarzschild and Kerr spacetimes using a Hamiltonian approach.

Contribution

It provides a detailed analysis of the integrability of spinning particle motion in black hole spacetimes, highlighting the effects of spin and spacetime geometry.

Findings

Spinning particle motion is generally non-integrable, indicating potential chaos.

The Hamiltonian formalism with linear spin approximation simplifies analysis.

Differences in integrability between Schwarzschild and Kerr spacetimes are discussed.

Abstract

The motion of a stellar compact object around a supermassive black hole can be approximated by the motion of a spinning test particle. The equations of motion describing such systems are in general non-integrable, and therefore, chaotic motion should be expected. This article discusses the integrability issue of the spinning particle for the cases of Schwarzschild and Kerr spacetime, and then it focuses on a canonical Hamiltonian formalism where the spin of the particle is included only up to the linear order.