Perturbation Method for Classical Spinning Particle Motion: I. Kerr Space-Time

Abstract

This paper presents an analytic perturbation approach to the dynamics of a classical spinning particle, according to the Mathisson-Papapetrou-Dixon (MPD) equations of motion, with a direct application to circular motion around a Kerr black hole. The formalism is established in terms of a power series expansion with respect to the particle's spin magnitude, where the particle's kinematic and dynamical degrees are expressed in a completely general form that can be constructed to infinite order in the expansion parameter. It is further shown that the particle's squared mass and spin magnitude can shift due to a classical analogue of radiative corrections that arise from spin-curvature coupling. Explicit expressions are determined for the case of circular motion near the event horizon a Kerr black hole, where the mass and spin shift contributions are dependent on the initial conditions of the particle's spin orientation. A preliminary analysis of the stability properties of the orbital motion in the Kerr background due to spin-curvature interactions is explored and briefly discussed.

23 pages; REVTeX file; 9 figures; Accepted for publication in Phys. Rev. D

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• Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds
• Fast Spinning Pulsars as Probes of Massive Black Holes' Gravity
• Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits
• Highly relativistic spinning particle starting near $r_{ph}^{(-)}$ in a Kerr field
• Stability of circular orbits of spinning particles in Schwarzschild-like space-times
• Complex orbital dynamics of a double neutron star system revolving around a massive black hole
• Perturbation Method for Classical Spinning Particle Motion: II. Vaidya Space-Time
• Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits
• Spinning test particles in the spacetime of a global monopole