Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds

Abstract

A new representation, which does not contain the third-order derivatives of the coordinates, of the exact Mathisson-Papapetrou-Dixon equations, describing the motion of a spinning test particle, is obtained under the assumption of the Mathisson-Pirani condition in a Kerr background. For this purpose the integrals of energy and angular momentum of the spinning particle as well as a differential relationship following from the Mathisson-Papapetrou-Dixon equations are used. The form of these equations is adapted for their computer integration with the aim to investigate the influence of the spin-curvature interaction on the particle's behavior in the gravitational field without restrictions on its velocity and spin orientation. Some numerical examples for a Schwarzschild background are presented.

21 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1105.2405

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• Highly relativistic circular orbits of spinning particle in the Kerr field
• Covariant hamiltonian spin dynamics in curved space-time
• Spinning bodies in curved space-time
• Tidal forces in dirty black hole spacetimes
• Fast Spinning Pulsars as Probes of Massive Black Holes' Gravity
• Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits
• Spin dynamics of a millisecond pulsar orbiting closely around a massive black hole
• Highly relativistic spin-gravity coupling for fermions
• Extreme mass ratio inspirals: perspectives for their detection
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• Highly relativistic spin-gravity-$\Lambda$ coupling
• Spinning bodies in General Relativity
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• Solutions of Mathisson-Papapetrou equations for highly relativistic spinning particles
• Gravitational orbital Hall effect of vortex light in Lense-Thirring metric
• Spinning Particles around Einstein-Geometric Proca AdS Compact Objects
• The effect of the WGC condition on the maximal energy extracted from black holes
• Numerical solution of Mathisson-Papapetrou-Dixon equations for spinning test particles in a Kerr metric
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