Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits

Abstract

The Mathisson-Papapetrou equations in the Schwarzschild background both at Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic circular orbits of a spinning particle in this background and dependence of the particle's orbital velocity on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle, which exist only for $r=1.5r_g(1+\delta )$, $0<\delta \ll 1$, the corresponding orbits of a spinning particle are allowed in a wider space region, and the dimension of this region significantly depends on the supplementary condition. At the Mathisson-Pirani condition new numerical results which describe some typical cases of non-circular highly relativistic orbits of a spinning particle starting from $r>1.5r_g$ are presented.

10 pages, 11 figures

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• Comparing Hamiltonians of a spinning test particle for different tetrad fields
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• Antigravity: Spin-gravity coupling in action
• Local Lorentz transformations and Thomas effect in general relativity
• Highly relativistic spin-gravity-$\Lambda$ coupling
• Hyperbolic-like elastic scattering of spinning particles by a Schwarzschild black hole
• Isofrequency pairing of spinning particles in Schwarzschild-de Sitter spacetime
• Spin effects and compactification
• Parameters of Innermost Stable Circular Orbits of Spinning Test Particles: Numerical and Analytical Calculations
• Nonequatorial circular orbits of spinning particles in the Schwarzschild-de Sitter background
• Solutions of Mathisson-Papapetrou equations for highly relativistic spinning particles
• On physics of a highly relativistic spinning particle in the gravitational field