Spinning particle in Schwarzschild's field: circular and other highly relativistic orbits

Details Spinning particle in Schwarzschild's field: circular and other highly relativistic orbits Spinning particle in Schwarzschild's field: circular and other highly relativistic orbits

2011-11-03

arxiv.org/abs/1111.0804v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 6 figures

Scientific paper

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 $r=1.5 r_g(1+\delta)$, $0<\delta \ll 1$, 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 $r>1.5 r_g$ are presented.

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