Dynamics of a spinning particle in a linear in spin Hamiltonian approximation
Abstract
We investigate for order and chaos the dynamical system of a spinning test particle of mass $m$ moving in the spacetime background of a Kerr black hole of mass $M$. This system is approximated in our investigation by the linear in spin Hamiltonian function [E. Barausse and A. Buonanno, Phys. Rev. D 81, 084024 (2010)]. We study the corresponding phase space by using 2D projections on a surface of section and the method of color and rotation on a 4D Poincar\'e section. Various topological structures coming from the nonintegrability of the linear in spin Hamiltonian are found and discussed. Moreover, an interesting result is that from the value of the dimensionless spin $S/(mM)={10}^{\ensuremath{-}4}$ of the particle and below, the impact of the nonintegrability of the system on the motion of the particle seems to be negligible.