Spin Precession of Dirac Particles in Kerr Geometry

TL;DR

This paper investigates how the intrinsic spin of Dirac particles precesses as they move along geodesics in Kerr black hole spacetime, emphasizing the role of observer frames and geometric symmetries.

Contribution

It provides a closed-form expression for spin precession in Kerr geometry using geometrically-defined reference frames, highlighting conditions where precession is absent.

Findings

Spin does not precess on the equatorial plane of Kerr geometry.

Reference frames can be constructed using local geometric information.

The results apply to both Kerr and Schwarzschild geometries.

Abstract

We isolate and study the transformation of the intrinsic spin of Dirac particles as they propagate along timelike geodesics in Kerr geometry. Reference frames play a crucial role in the definition and measurement of the intrinsic spin of test particles. We show how observers located in the outer geometry of Kerr black holes may exploit the symmetries of the geometry to set up reference frames using purely geometric, locally-available information. Armed with these geometrically-defined reference frames, we obtain a closed-form expression for the geometrically-induced spin precession of Dirac particles in the outer geometry of Kerr black holes. We show that the spin of Dirac particles does not precess on the equatorial place of Kerr geometry; and hence, in Schwarschild geometry.