Investigating spinning test particles: spin supplementary conditions and the Hamiltonian formalism

Abstract

In this paper we report the results of a thorough numerical study of the motion of spinning particles in Kerr spacetime with different prescriptions. We first evaluate the Mathisson-Papapetrou equations with two different spin supplementary conditions, namely, the Tulczyjew and the Newton-Wigner, and make a comparison of these two cases. We then use the Hamiltonian formalism given by Barausse, Racine, and Buonanno in [Phys. Rev. D, 80, 104025 (2009)] to evolve the orbits and compare them with the corresponding orbits provided by the Mathisson-Papapetrou equations. We include a full description of how to treat the issues arising in the numerical implementation.

arXiv comment17 pages, 11 figures, accepted for publication in PRD

References in corpus (21)

• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• An improved effective-one-body Hamiltonian for spinning black-hole binaries
• Chaos in Schwarzschild Spacetime : The Motion of a Spinning Particle
• Hamiltonian of a spinning test-particle in curved spacetime
• Lyapunov indices with two nearby trajectories in a curved spacetime
• Gravitational waves from a spinning particle in circular orbits around a rotating black hole
• ADM canonical formalism for gravitating spinning objects
• Dynamics of spinning test particles in Kerr spacetime
• Motion of spinning test bodies in Kerr spacetime
• A survey of spinning test particle orbits in Kerr spacetime
• Influence of internal structure on the motion of test bodies in extreme mass ratio situations
• Canonical Formulation of Spin in General Relativity
• Mathisson's helical motions for a spinning particle --- are they unphysical?
• Periastron advance in spinning black hole binaries: comparing effective-one-body and Numerical Relativity
• Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries
• Free motion around black holes with discs or rings: between integrability and chaos - III
• A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
• Frenkel electron and a spinning body in a curved background
• Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime
• Gauss collocation methods for efficient structure preserving integration of post-Newtonian equations of motion
• Adjusting chaotic indicators to curved spacetimes

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