The Frenet Serret Description of Gyroscopic Precession

TL;DR

This paper uses Frenet-Serret formalism to analyze gyroscopic precession in various spacetimes, providing new formulae and insights into the geometric nature of precession phenomena.

Contribution

It introduces a novel geometric approach to gyroscopic precession using Frenet-Serret formalism in diverse spacetime backgrounds.

Findings

Derived general precession formulae for circular orbits.

Analyzed precession in Kerr, Schwarzschild, Minkowski, De Sitter, and G"odel spacetimes.

Connected precession to congruence vorticity and spacetime symmetries.

Abstract

The phenomenon of gyroscopic precession is studied within the framework of Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to the congruence vorticity is highlighted with particular reference to the irrotational congruence admitted by the stationary, axisymmetric spacetime. General precession formulae are obtained for circular orbits with arbitrary constant angular speeds. By successive reduction, different types of precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime family. The phenomenon is studied in the case of other interesting spacetimes, such as the De Sitter and G\"{o}del universes as well as the general stationary, cylindrical, vacuum spacetimes.