On common solutions of Mathisson equations under different conditions

In the context of investigations of possible highly relativistic motions of a spinning particle in the gravitational field, which can be described by the Mathisson equations under different supplementary condition, we analyze the circular orbits in a Schwarzschild field. The very orbits most clearly...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2008-03
Main Authors: Plyatsko, Roman, Stefanyshyn, Oleksandr
Format: Article
Language:English
Subjects:
Circular orbits
Gravitational effects
Gravitational fields
Mathematical analysis
Orbits
Particle spin
Relativism
Relativistic effects
Spin-orbit interactions
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the context of investigations of possible highly relativistic motions of a spinning particle in the gravitational field, which can be described by the Mathisson equations under different supplementary condition, we analyze the circular orbits in a Schwarzschild field. The very orbits most clearly demonstrate the effect of the gravitational spin-orbit interaction on the particle's motion. It is shown that the Mathisson equations under the Frenkel-Mathisson and Tulczyjew-Dixon conditions have the common solutions describing the highly relativistic circular orbits in the region \(r=3M(1+\delta), |\delta|\ll 1\). These orbits essentially differ from the geodesic circular orbits in the same region, particularly by the value of the particle's energy on the corresponding orbits.
ISSN:2331-8422