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 Poincare 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(-4) of the particle and below, the impact of the nonintegrability of the system on the motion of the particle seems to be negligible.