Coupling Between the Spin and Gravitational Field and the Equation of Motion of the Spin

TL;DR

This paper derives the spin's equation of motion within gauge theory of gravity, showing it aligns with general relativity's predictions in the post-Newtonian approximation, especially regarding gyroscope precession.

Contribution

It introduces a spin equation of motion in gauge gravity and demonstrates its consistency with general relativity in the post-Newtonian limit.

Findings

The gauge theory of gravity predicts the same gyroscope precession as general relativity.

The derived spin equation reduces to the parallel transport equation in the post-Newtonian approximation.

The results support the compatibility of gauge gravity with established gravitational phenomena.

Abstract

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry can not be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field, an equation of motion of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives out the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.