Ultrarelativistic circular orbits of spinning particles in a Schwarzschild field described by the Mathisson-Papapetrou equations are considered. The preliminary estimates of the possible synchrotron electromagnetic radiation of highly relativistic protons and electrons on these orbits in the gravitational field of a black hole are presented
It is shown that the gravitational ultrarelativistic spin-orbit interaction violates the weak equivalence principle in the traditional sense. This fact is a direct consequence of the Mathisson-Papapetrou equations in the frame of reference comoving with a spinning test body. The widely held assumption that the deviation of a spinning test body from a geodesic trajectory is caused by tidal forces is not correct. PACS number(s): 04.20.Cv. 95.30.Sf
The Mathisson-Papapetrou equations in Schwarzschild's background both at the Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic planar 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 = 1.5rg(1 + δ), 0 < δ ≪ 1, the corresponding orbits of a spinning particle are allowed in a wider space region, and the dimension of this region essentially depends on the supplementary condition. At the Mathisson-Pirani condition new numerical results which describe some typical cases of noncircular highly relativistic orbits of a spinning particle starting from r > 1.5rg are presented. PACS numbers: 04.20.-q, 95.30.Sf I.
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.PACS numbers: 95.30.Sf
The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz γ-factor on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle the corresponding orbits of a spinning particle are allowed in much wider space region. Some of these orbits show the significant attractive action of the spin-gravity coupling on a particle and others are caused by the significant repulsive action. Numerical estimates for electrons, protons and neutrinos in the gravitational field of black holes are presented.
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