Gyroscopic precession in non-circular orbits: a phase-locked tetrad approach

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Spin, Gyroscopic Precession, Tetrad Formalism

Scientific paper

We deduce the explicit form of a phase-locked (PL) tetrad, adapted to a small spinning particle (a test gyroscope) following an arbitrary geodesic orbit in the Schwarzschild geometry of a gravitational source. We subsequently obtain the analytic expression of the gyroscopic precessional velocity Ω in a non-circular orbit, by means of the Fermi rotation coefficients related to the tetrad’s transport law. As an application, we compute the orbital shift in the spin vector, considering a spinning test particle (the gyroscope) in a slightly non-circular orbital motion in the weak gravitational field limit. We compare our results with those of other previous works.

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