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

TL;DR

This paper investigates the existence and properties of highly relativistic spinning particle orbits in Schwarzschild spacetime, revealing that spin allows for a wider range of stable orbits compared to spinless particles, with new numerical results for non-circular orbits.

Contribution

It provides a detailed analysis of highly relativistic spinning particle orbits in Schwarzschild spacetime, including the effects of different supplementary conditions and new numerical results for non-circular trajectories.

Findings

Spinning particles have a wider region of highly relativistic circular orbits than spinless particles.

The orbital velocity depends on the particle's spin and radial coordinate.

New numerical results describe non-circular highly relativistic orbits starting beyond $1.5 r_g$.

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