Kerr Solution Consistent Motion of Spin Particles in the General Relativity

TL;DR

This paper derives equations for the spin evolution of particles in general relativity using the Einstein-Infeld-Hoffmann method, revealing new insights into spin dynamics and angular momentum conservation.

Contribution

It introduces a novel derivation of spin evolution equations in the post-Newtonian approximation using harmonic coordinates and Kerr solutions, highlighting differences from previous models.

Findings

Deviation of gyroscope axis is half and opposite in direction compared to previous results.

Total angular momentum of spin particles is generally not conserved.

Derived equations improve understanding of spin dynamics in relativistic systems.

Abstract

The paper presents equations determining the particle spin evolution in the post-Newtonian approximation in the problem of motion of two mass and spin possessing particles. The equations are derived with the Einstein-Infeld-Hoffmann method from the condition of metric tensor symmetry. The consideration uses the condition of coordinate harmonicity and the metric coincidence nearby the particles with expansions of the Kerr solution written in the harmonic coordinates. For gyroscopes on satellites Gravity Probe B, for example, the equations yield a deviation of the axis of revolution, which is, first, two times as small as that obtained by J.L.Anderson in paper gr-qc/0511093 and, second, the deviation is of opposite sense. From the equations it follows that the total angular momentum of the spin particle system, generally speaking, is not conserved, beginning even with the post-Newtonian approximation. The results are briefly discussed.