Black hole geodesic parallel transport and the Marck recipe for isolating cumulative precession effects

TL;DR

This paper rederives Wigner rotations from a relative boost perspective and applies them to analyze gyroscope spin precession along Kerr spacetime geodesics, clarifying the geometric aspects of Marck's parallel transport method.

Contribution

It provides a new geometric interpretation of Marck's recipe for parallel transport and isolates the cumulative precession effects in Kerr spacetime.

Findings

Explicit calculation of precession effects for bound and unbound equatorial geodesics.

Clarification of the geometric properties of spin precession in Kerr spacetime.

Reinterpretation of Wigner rotations in the context of gyroscope precession.

Abstract

The Wigner rotations arising from the combination of boosts along two different directions are rederived from a relative boost point of view and applied to gyroscope spin precession along timelike geodesics in a Kerr spacetime, clarifying the geometrical properties of Marck's recipe for describing parallel transport along such world lines expressed in terms of the constants of the motion. His final angular velocity isolates the cumulative spin precession angular velocity independent of the spacetime tilting required to keep the spin 4-vector orthogonal to the gyro 4-velocity. As an explicit example the cumulative precession effects are computed for a test gyroscope moving along both bound and unbound equatorial plane geodesic orbits.