The 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 provided in [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 Poincaré section. Various topological structures coming from the non-integrability 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 non-integrability of the system on the motion of the particle seems to be negligible.

11 pages, 8 figures, 1 table, to appear in Phys. Rev. D

References in corpus (5)

• Free motion around black holes with discs or rings: between integrability and chaos - II
• Free motion around black holes with discs or rings: between integrability and chaos - I
• Investigating spinning test particles: spin supplementary conditions and the Hamiltonian formalism
• The phase-space of boxy-peanut and X-shaped bulges in galaxies I. Properties of non-periodic orbits
• The phase-space of boxy-peanut and X-shaped bulges in galaxies II. The relation between face-on and edge-on boxiness

Cited by in corpus (4)

• Dynamics of extended bodies with spin-induced quadrupole in Kerr spacetime: generic orbits
• Spinning particle orbits around a black hole in an expanding background
• The Phase Space Structure in the vicinity of vertical Lyapunov orbits around L1,2 in a barred galaxy model
• Minimal Length Effects on Motion of a Particle in Rindler Space