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.

17 pages, 11 figures, accepted for publication in PRD

References in corpus (6)

• Lyapunov indices with two nearby trajectories in a curved spacetime
• ADM canonical formalism for gravitating spinning objects
• Motion of spinning test bodies in Kerr spacetime
• Canonical Formulation of Spin in General Relativity
• Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries
• A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems

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• General treatment of quantum and classical spinning particles in external fields
• Spin supplementary conditions for spinning compact binaries
• The dynamics of a spinning particle in a linear in spin Hamiltonian approximation
• Time parameterizations and spin supplementary conditions of the Mathisson-Papapetrou-Dixon equations
• Motion of a spinning particle around an improved rotating black hole
• Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations
• Effect of Particle Spin on Trajectory Deflection and Gravitational Lensing
• Spinning particle orbits around a black hole in an expanding background
• Motion of Spinning Particles around Black Holes
• Acceleration of particles in Schwarzschild and Kerr geometries