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

TL;DR

This study compares different spin supplementary conditions and Hamiltonian formalism for simulating the motion of spinning particles in Kerr spacetime, providing insights into their numerical implementation and differences.

Contribution

It offers a comprehensive numerical comparison of Mathisson-Papapetrou equations with Tulczyjew and Newton-Wigner conditions and the Hamiltonian approach in Kerr spacetime.

Findings

Differences between Tulczyjew and Newton-Wigner conditions are characterized.

Hamiltonian formalism results are compared with Mathisson-Papapetrou equations.

Numerical implementation issues are thoroughly addressed.

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.