Solutions of Mathisson-Papapetrou equations for highly relativistic spinning particles

Abstract

Different types of essentially nongeodesic motions of highly relativistic spinning particles in Schwarzschild's and Kerr's background which follows from the Mathisson-Papapetrou (MP) equations are considered. It is shown that dependently on the correlation of signs of the spin and the particle's orbital velocity the spin-gravity coupling acts as a significant repulsive or attractive force. Numerical estimates for electrons, protons, and neutrinos in the gravitational field of black holes are presented. The correspondence between the general relativistic Dirac equation and MP equations is discussed. It is stressed that for the highly relativistic motions the adequate supplementary condition for the MP equations is the Mathisson-Pirani condition. In the following it is important to study the possible role of the highly relativistic spin-gravity coupling in astrophysics, cosmology, and high energy physics.

13 pages, 8 figures. Invited contribution as part of the Springer series "Fundamental Theories of Physics", v.179 (2015), "Equations of Motion in Relativistic gravity", D. Puetzfeld et al. (eds.), p. 165-190

References in corpus (7)

• Spin dynamics in gravitational fields of rotating bodies and the equivalence principle
• Can gravitation accelerate neutrinos?
• Highly relativistic circular orbits of spinning particle in the Kerr field
• Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds
• Dirac equations in curved space-time versus Papapetrou spinning particles
• Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits
• Highly relativistic spinning particle starting near $r_{ph}^{(-)}$ in a Kerr field

Cited by in corpus (2)

• Nonequatorial circular orbits of spinning particles in the Schwarzschild-de Sitter background
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