Spinning particles moving around black holes: integrability and chaos

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.Comment: 6 pages, 2 figures, to appear in the Proceedings of the "14th Marcel Grossmann Meeting" (Rome, July 12 - 18, 2015

Growth of orbital resonances around a black hole surrounded by matter

This work studies the dynamics of geodesic motion within a curved spacetime around a Schwarzschild black hole, perturbed by a gravitational field of a far axisymmetric distribution of mass enclosing the system. This spacetime can serve as a versatile model for a diverse range of astrophysical scenarios and, in particular, for extreme mass ratio inspirals as in our work. We show that the system is non-integrable by employing Poincar\'e surface of section and rotation numbers. By utilising the rotation numbers, the widths of resonances are calculated, which are then used in establishing the relation between the underlying perturbation parameter driving the system from integrability and the quadrupole parameter characterising the perturbed metric. This relation allows us to estimate the phase shift caused by the resonance during an inspiral.Comment: 11 pages, 3 figures, 1 table, Proceedings of RAGtime 23-25. Edited by Z. Stuchl\'ik, G. T\"or\"ok and V. Karas. Institute of Physics in Opav